Solve calculus and algebra problems online with Cymath math problem solver with steps to show your work. Get the Cymath math solving app on your smartphone! Learn linear algebra for free—vectors, matrices, transformations, and more. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains.kastatic.org and.kasandbox.org are unblocked. Engaging math books and online learning for students ages 8-13. Pages in category 'Algebra Problems' This category contains only the following page. 2006 iTest Problems/Problem 36. Category: Math Problems; Art of Problem Solving is an ACS WASC Accredited School. AoPS Online Beast Academy AoPS Academy. Intermediate Algebra Problems With Answers - sample 2:Find equation of line, domain and range from graph, midpoint and distance of line segments, slopes of perpendicular and parallel lines. Intermediate Algebra Problems With Answers - sample 3: equations and system of equations, quadratic equations, function given by a table, intersections of.

• Algebra Imath Problem Solving Problems
• Free Algebra Word Problem Solver

Remember this kind of problem from primary school?

? + 5 = 7

We just needed to figure out which number should go into the box to make it a true statement. Clearly, we need to replace the question mark with '2':

2 + 5 = 7

Solving equations using algebra is really no different. Instead of using a box, we use a letter to represent a number. Our task is to find the correct number (or sometimes there may be more than one number) that makes the equation true.

Sometimes we can 'see' the right answer if it is simple (maybe we can just count up with our fingers, or whatever.) But when our equations become more complicated, we need a process to follow that will eventually give us the answer.

Our Process

1. We are aiming to get x (or whatever letter the question uses) on the left hand side of the equals sign, by itself.
2. We solve equations by balancing: whatever we do to one side of an equation, we must do the same to the other side. So if we add 4 to the left hand side, we must add 4 to the right hand side as well. If we multiply on the left side by 2, we multiply on the right side by 2 as well.
   

Example 1

Solve the equation

x − 6 = 10

Answer

We need to 'get rid of' the -6 on the left hand side so we are left with x only on the left hand side.

The opposite of subtracting 6 is adding 6.

If we add 6 to both sides, we will remove the -6 on the left.

x − 6 = 10

x − 6 + 6 = 10 + 6

x = 16

So the value of x needs to be 16 to make the equation true.

CHECK into the original question:

16 − 6 = 10. It checks out okay.

Example 2

Solve 5x = 35

Answer

This time we are answering

5 × ? = 35

We could do this in our heads easily (right?), but if the problem is more complicated, we need to know what to do.

On the left, we are multiplying our unknown quantity by 5. We'll use 'x' for this quantity.

`5x = 35`

The opposite of multiplying by 5 is dividing by 5. So we divide both sides by 5:

`(5x)/5=35/5`

We obtain :

`x = 7`

CHECK: 5 × 7 = 35. It checks out okay.

[These checks seem silly with easy examples, but it is a really good idea to check your solutions for all the equation problems that you do. It means you can leave the problem feeling good that you have the right answer and also, you learn more about how the solution works.]

Example 3

Solve

`(3x)/4=7`

Answer

This time we need to do 2 steps to solve the equation. We notice there is a 4 on the bottom of the fraction.

`(3x)/4=7`

This is equivalent to dividing by 4. The opposite to dividing by 4 is multiplying by 4. So we do that first:

`(3x)/4 xx 4=7xx4`

Cancelling the 4's on the left gives:

`3x=28`

In the middle step we cancelled out the 4's, so we are left with no fraction.

Now we need to divide both sides by 3, since we have a '3×' on the left hand side of the equation.

`x=28/3=9 1/3`

Some countries (like the USA) will leave the answer as a single fraction (28/3), while the practice in other countries (like the UK and Australia) is to express the answer as a mixed numeral.

CHECK:

Is our answer correct?

Substituting our answer in the left hand side gives:

`(3x)/4=3/4 x=3/4 xx 28/3`

Canceling the 3's (which gives us 1) and the 28 with the 4 gives us 7:

`3/4 xx 28/3 = 7`

The right hand side in the question was 7, so we are confident our answer is correct.

Example 4

Solve 5 − (x + 2) = 5x

Answer

First, we expand out the bracket.

`5 - (x + 2) = 5x`

`5 - x - 2 = 5x`

`3 - x = 5x`

Now we recognise that it is easier to get all the x's on the right side, by adding x to both sides :

`3 = 6x`

Now I divide both sides by 6 and swap the sides:

`x = 0.5.`

CHECK:

We check our answer in both sides of the equation. If it works, it must be the right answer.

LHS = `5 - (0.5 + 2) = 2.5`

RHS = `5 xx 0.5 = 2.5` = LHS.

Checks OK.

Example 5

Solve 5x − 2(x − 5) = 4x

Answer

Expanding the bracket:

`5x - 2(x - 5) = 4x`

`5x - 2x + 10 = 4x`

`3x + 10 = 4x`

Subtracting `3x` from both sides and swapping sides gives:

`x = 10`

CHECK:

LHS = `5 xx 10 - 2(10 - 5) = 50 - 10 = 40`

RHS = `4 xx 10 = 40` = LHS.

Checks OK.

Example 6

If you can, solve the equation

− (7 − x) + 5 = x + 7

What do you conclude?

Answer

− (7 − x) + 5 = x + 7

Expand out the brackets:

−7 + x + 5 = x + 7

Subtract x from both sides:

`-7+5=7`

Simplify the left hand side:

`-2 = 7` ????

This is not possible, so we conclude that there are no possible values for x.

[There was a hint in the question that something funny may be going on. Always be aware that an equation may not have solutions. Also, there are times when you get solutions that cannot possibly work, so you have to discount them. We find such examples later in Equations with Radicals.]

Mathematics is regarded as the monster that haunts the dreams of countless students from all around the world. Whether you’re in middle school, high school, college, or even starting out with your job, chances are the idea of solving math problems sends shivers down your spine every time.

One field that’s particularly known (and often feared) by math students is algebra. The great frustration that this subject spreads is mainly due to the fact that it mixes numbers, letters, and symbols in equations and formulas, thus making them look more complicated than they really are.

If you have some algebra homework that you need to solve, or need to help your kid with a complicated problem or equation, you can use our algebra math calculator, which is an app designed to help students understand their mistakes and get over them through continuous practice.

Instead of listing the arguments that support learning algebra, we’re going to debunk the arguments that are against this amazing mathematical field.

Why Learn Algebra If I’m Not Considering College?

In the past, teachers used to accord students into “convenient” culture-based tracks, thereby minimizing the chances of many children of attending college before they’d even start high school.

Are you an Asian student? You should study math.

Are you an African-American student? You’re better off mastering basketball.

Are you a white American student? Maybe try with history or art.

Basically, anyone who wasn’t regarded as smart enough would be appointed to what you’d call “consumer math” — the low-tier math that is often thought of to be appropriate for average students.

Thankfully, those days are over, and education is now free to all. It would be horrible to see a second rise of the days in which one’s role in life was decided based on their name, skin color, or social status.

Even if you’re not considering college, don’t limit your potential by classifying yourself as “not smart enough” and therefore assuming that you’ll find no use for algebra.

Studying Algebra is Stupid

Have you ever asked yourself why do people always complain about math and science? Is it because they require a lot of discipline and dedication? Or because they’re difficult to understand?

Have you ever noticed that no one asks why you have to take physical education or English literature classes, even though math, physics, and science are much more critical to the founding of the modern society than Shakespeare or the techniques of shooting a three-pointer?

Education has to be fun, easy, and entertaining in order for it to be acceptable, or so says the modern American educationist philosophy.

Today’s students believe that if a subject requires some effort, they shouldn’t have to take it. Little do they know that the most beneficial things in life demand making some effort.

If you want an excellent job, an alluring career, a limitless future, you’ll most definitely be in need of some mathematical skills, and when you say math, you say algebra.

Have you ever thought about why do you hit the gym regularly? Is it because lifting weights is effortless? Or because you want to get better, challenge yourself, build your strength, and prepare your body for whatever you might encounter in life?

Why do people cycle or jog? Is it because it’s fun to sweat bullets and get knee soreness? If I were to guess I would say that they do it because they want to be healthy and strong in order to resist diseases and be ready for whatever health obstacle life may throw their way.

If you want your mind and brain to be sharp as well, you have to train it and prepare it for real-life problems.

So, our only advice here is to practice, practice, and practice, and if you ever find yourself stuck, remember that our calculator for algebra is here to help you get over any obstacle during your math-learning journey.

I’m Only Taking Algebra Because the Uni Forced Me

Let’s be clear for a moment; the dean didn’t put a knife on your throat to force you to enroll. You, and only, are the one who decided to join to get your diploma.

Perhaps you wanted to get a great job, and in order for you to get it, you needed some mathematical skills that include algebra.

Maybe you won’t have to factor any quadratic for the rest of your life, but you do need your diploma, and you have to do whatever it takes to obtain it.

The algebra class is necessary to pass if you want to achieve that goal. If you decide to skip it, it’s all right, but you won’t get that degree of yours. It’s your decision after all.

My Career Won’t Require Algebra

One of the many differences between a college graduate and a trained employee is the student’s capability of a deeper understanding of the situation and a better ability to build links and connections and acquire new skills.

You certainly won’t need everything you learned in algebra, but does this imply that you should drop out of your college and only get the training that’s required for the job you seek to take?

I’m sure your answer goes along the lines of “I can’t afford to drop out, I can’t be qualified for that job without a college diploma or degree”.

So, in order for you to get your dream job, you need to prove yourself and capabilities through a particular skill set, but to really display that proficiency, you need a college degree. To obtain that degree, you need algebra. Algebra, in other words, is a must if you want the job.

Math people have a common saying that goes along the lines of “one truly learns arithmetic and pre-algebra in algebra and algebra and trigonometry in calculus”. The meaning behind all of this is that one truly gets a better understanding of a specific material once they have to use it in different situations.

So, even if you’re right, even if you turn out after a thirty or forty-year career, never to have resorted to algebra problem-solving skills, it’s still a brilliant idea to have gone through this class before beginning your career. Why? Because algebra is essential for real-life problems, be it by performing basic arithmetic operations, understanding negative numbers, or working with percentages.

Take your algebra class, practice using our algebra simplify calculator, and you’re bound to master those skills.

Will I Really Need Algebra in Real Life?

Sadly, we cannot answer that question for you. It’s not a simple yes-or-no situation.

Think of the rate of “non-traditional” students retaking math classes, and all the old people returning to uni after years of dropping out, even though they don’t need algebra for their jobs.

The very fact that they are studying algebra all these years after high school highly indicates that they haven’t used algebra a lot since the time they finished their studies. They made it this far without needing algebra, but here they are returning back to the very college seats they abandoned years ago because they felt the necessity of such a subject.

Take into consideration that you didn’t learn the alphabet back in kindergarten because you knew you’d be studying Shakespeare’s plays this year. The same goes for algebra; you don’t study it because you know that you’ll be interpreting graphs and working with quadratics in a few years, you study it to build the cornerstone for bigger things to come, and to help create better opportunities for yourself in the future.

Algebra is the key to various domains no matter how big or small they are.

For instance, let’s assume that your job requires working with spreadsheets filled with formulas. For that, you need a basic understanding and enough knowledge of variables and equations.

Also, if you find yourself in a meeting that involves working with graphs, charts, and tables, you’ll need to interpret them in an intelligent manner if you’re looking to stand your ground during the discussion. The only way to do so is by having the least of knowledge in algebra.

How Relevant Will Algebra Be in the Years to Come?

It’s undeniable that jobs will require different skill-sets in twenty or thirty years from now, but the only thing that’ll remain constant is mathematics. One plus one will always equal two.

Sure, you’ll receive the required training for any job you’ll get, but you still need a decent knowledge and skillset to get that job in the first place. To be on pace with the progress, to remain on top of the ladder, and to open up for better future opportunities, you need the strong foundation that mathematics provides.

The lessons and patterns taught by mathematics are vital. Learning formulas and variables, interpreting graphs and tables, and thinking logically to find solutions are essential skills that will prove to be useful for the rest of your life. They are not things that you learn in school just to pass a test; they’re an arsenal of capabilities that, if mastered, will yield great results for both your professional and personal life.

So, that’s it; those are the reasons why learning and studying algebra is essential no matter where you are in your educational (or professional) ladder.

While it’s possible to get by using a standard scientific calculator, using our Algebra Calculator can be a better choice if:

• You need an algebra calculator with steps

I wish I could find an algebra calculator that shows work when I was younger. That would’ve made my math journey a lot easier.

Whether you’re trying to solve your homework, verify your answer, or help your kid with his/her assessment, getting your hands on a calculator that can show the work needed to get to the result can be highly beneficial, as that’s a great way to identify your mistakes and work on improving them.

Just remember to work on your own before checking the solution. Otherwise, you’d only be cheating yourself (or your kid).

• You need an online algebra calculator

While there are many downloadable calculator apps available on the internet, there’s still a great chance that they’re not compatible with your device.

Being an online app, our matrix algebra calculator can work on any smartphone, tablet, or computer as long as it has a decent internet connection.

• You need a free algebra calculator

We all know how expensive a tutor can be, and while a scientific calculator doesn’t cost that much, it cannot help you identify your mistakes as it’s only programmed to display the result.

Our tool, on the other hand, gets you the best of both worlds, a free alternative to both tutors and scientific calculators that can solve any equation you throw at it while showing you the step-by-step process that led to the result to help you better understand your errors.

• You need a function-oriented calculator

Trying to get a grasp of a scientific calculator can be a real pain in the neck, which raised the need for a function-oriented app that focuses on specific applications.

So, whether you want an algebra square root calculator, an algebra factor calculator, or a simplify boolean algebra calculator, Mathway’s tool got you covered.

I believe this is self-explanatory. Gone are the days when people used to find offline solutions for their problems. The online era began some years ago, and it isn’t going to end any time soon.

Being an online tool, our fraction algebra calculator can be accessed from anywhere as long as you have an internet connection, and you don’t need to download or install anything to run it, making it compatible with any device.

On the train and want to practice some problem-solving? Pull your phone and do so.

Watching a movie on your laptop and remembered your homework? Open a browser tab, access our app, and work on your assessment.

Want your kids to do something useful with their tablets? Bookmark our app’s page and reward them whenever they solve a problem correctly.

As you can clearly see, it’s only natural for our tool to be an online one.

Have you had any math problems keeping you up at night? Well, if you do, you’ve hopefully found the place that’s going to give you the solution for more than just one problem. Here, we are presenting you with the tool that will make your algebra worries a thing of the past.

We couldn’t help but notice all the students’ frustration over their math homework. Not only does it make school work dull and unexciting, but it also deters youngsters from seeking knowledge with the passion that they need to have. So for all the tired mathematical souls across the globe, we bring you a service that will hopefully boost your level and improve your skills in all-things algebra. Here is the online, free to use algebra calculator you’ve been waiting for.

Well, there’s no way around it really but to say it as it is: This app will give you the ability to do, pretty much, everything you can imagine when it comes to algebra. Primarily, it can work as a:

• Linear algebra calculator
• Algebra 1 calculator
• Algebra 2 calculator
• College algebra calculator
• Step by step algebra calculator
• Algebra graphing calculator
• Algebra answers calculator
• Boolean algebra calculator
• Algebra factoring calculator
• Algebra equation calculator

Because it packs a lot of versatile tools and seeing how it is suitable for different levels of education, this calculator isn’t just a good one for algebra; it’s probably the best algebra calculator out there. It even doubles as a pre algebra calculator among others, can you believe that?

Access the app and take a quick look at the display on this thing. You’ll be able to see that it comes with a wide range of buttons and symbols. Sure, a bunch of them can be found on any regular calculator you can get your hands on, but you’ll also notice a number of other tools, uniquely made for this specific app.

The list is too long to be included entirely, but rest assured knowing that this app provides things like square roots, exponents, fractions, absolute value, parenthesis, division sign, rectangular pyramids, cylinder, trapezoid, triangle, equal to or less than, etc. I think that’s enough things to list to prove just how versatile this app is.

It’s a magnificent tool for doing math relating to pre-calc and algebra 2, and it’s also the best graphing calculator you can find for algebra.

It can be very useful for answer verification, testing, and homework because of its incredible multi-functionality. It offers the user a chance to test their own abilities and knowledge in mathematical fields.

Wherever you are and whenever you feel the need to give yourself a challenge, take your phone and open the app to evaluate yourself. You don’t even need to bring your own problems as you’ll find a list of them included with the app.

Finding a book on how to use a calculator for beginners is highly unlikely. Going through endless search results on the matter would be as tiresome as trying to solve a mathematical problem. Because of that, we’ll try to help you out by giving you a quick and simple walkthrough of how to use the app just to save you some time. The app is very easy to use, as long as you know the following:

• You’ll find existing examples for you to use in typing your mathematical expression. Or if you’d like, you can do so manually through the symbols.
• Of course, you’ll want to see the expression in the usual mathematical format. For that, you would have to click on the “show” button. In case you stumble upon any issues, click the “?” for help.
• The app is programmed to figure out what kind of problem you have through the expression that you’ve typed in. But in case it doesn’t get the correct type, you have the option to choose it by yourself
• Clicking the “Answer” button will get the app to do its problem-solving. You just sit there and wait.

And voila, you have your answer. All you have to do now is check the answer to verify your attempt at solving the problem and compare it with the result given by the app. This is a helpful method for identifying your mistakes and avoiding them in the future. If you need to see the full steps, you’ll need to sign up for Mathway.

Remember, don’t check the result until you’ve tried solving the problem yourself. This app was designed to help you understand your mistakes and get over the obstacles that may come your way, not to do your work for you.

This is the innovative creation of the folks at Mathway. The reason we have it here on our page to make it easily accessible to everyone. A simple sign up is required for unlocking all of the utilities of the app, but that won’t be a big deal. The process is rather simple and short. If you’re under 18, be sure to get parental approval before signing up for the Mathway algebra calculator.

This doesn’t really need any more praise. The app speaks for itself. It’s time for all students to surpass the obstacles that they face daily because of tedious algebra problems and this app can help do that. Whenever you need, come to our website, start the app and train to become a better problem-solver. This algebra graphing calculator will make sure of that.

Welcome to the algebra calculator, an incredible tool that will help double-check your work or provide additional practice to prepare for tests or quizzes.

Homework Check: Our algebra calculator can help you check your homework. Simply enter your problem and click Answer to find out if you worked the problem correctly. Now, I hope you realize that if you simply put your homework problems into the calculator and copy the answer down, you’re cheating yourself in the long run because you haven’t really learned anything. In order to do well on your upcoming tests and quizzes, you need to understand where the answer came from. That way, you can find your mistakes and learn how to complete the problems correctly. That’s why we’re encouraging you to sign up for Mathway, a supportive tool which provides you with the complete steps used to solve each problem. Ask your parents about it – it’s much cheaper than tutoring and will be a good investment in your future. Just click View Steps on the answer page to sign up.

Prepare for tests and quizzes by practicing extra problems. Simply locate a topic you wish to review in the Examples section of the calculator. An example problem will appear in the calculator. (If you’re confused by the notation in the box, click the Show button. This shows the problem in the standard mathematical format.) Solve the problem on a separate sheet of paper and write down your answer. Then check your answer using the calculator – just make sure the Select Topic section matches what you’re practicing. If you got the answer correct, great! If not, you’ll want to view the steps in order to find your mistake. Sign up for Mathway (or ask your parents to sign you up) and you’ll be able to find your errors and see how to complete the problem correctly. It’s definitely worth the investment as you can use this calculator to prepare for tests for the rest of the year.

1. Enter the problem either using the symbols or by starting with an example.

2. You can make sure you entered your problem correctly by clicking the Show button next to Math Format. This will show your problem in the format you’re used to seeing. If it looks wrong and you need more help, click the ? Box next to the Enter Problem field.

3.The Select Topic dropdown will automatically populate with the most common type of problem, but if you want the calculator to do something different, just choose the correct option from the dropdown.

4. Click Answer to view the answer.

5. In order to see the steps, sign up for Mathway.

Using an example:

Scroll through the topics to find the type of problems you are wanting to check or practice. This will provide an example in the calculator so that you can see how it is formatted. You can then change the numbers or variables to fit the problem you are trying to check.

Parenthesis – They indicate multiplication or that the operation inside should be done first.

Brackets – Use brackets if you need a parenthesis within parenthesis – The brackets go on the outside as seen in this example: [3 + 2(10 -1)] ÷ 7.

[frame align=”left”]Absolute Value – The absolute value tells how far away a number is from zero. It’s always the same number but positive. For example, |3| is 3 and |-3| is also 3.

Fractions – Type the numerator and denominator inside the parenthesis that will come up. To create a mixed number, delete the parenthesis and put a space between the whole number and the numerator of the fraction. For example, for 2¼ type 2 1/4.

Exponents – Type the base before the ^ symbol and the exponent in parenthesis. For example, 5^(2) for 5². Remember that the exponent tells how many times the base is multiplied by itself.

[frame align=”left”]

Subscripts – Your variable goes outside the bracket and the subscript inside. For example, x₁ would be x[1]. Remember that subscripts are used to specify which variable you are using.

Square Roots – Type the radicand (the number inside the square root symbol) inside the parenthesis. Square roots find what number times itself equals the radicand. For example, the square root of 49 is 7 because 7 * 7 = 49.

Other Roots – Type the index after the √ symbol and the radicand inside the parenthesis. For example, use √3:(8) for . Remember that a different index means that the answer must be multiplied by itself that many times to equal the radicand. In our example, 2 * 2 * 2 = 8, so 2 would be the answer because 2 times itself 3 (the index) times is 8.

Note: If no index is given, it is assumed to be two and is just called a square root.

Matrices – Separate the entries in each row by commas and put a _ between rows. For example, the matrix would be entered as matrix[1,-2_5,7].

Coordinates – Type a coordinate as you normally would – such as (1,5).

Functional Notation – Type functional notation as you normally would. Remember that f(x) is pronounced “f of x” and typically replaces y in an equation.

Natural Logarithm – Type the number inside the parenthesis. Remember that a natural logarithm answers the following question: e to what power equals the given number. The constant e is approximately equal to 2.718.

Logarithm –

Type the number inside the parenthesis. A logarithm with no subscript (such as the one seen here) answer the question “10 to what power equals the number given.” For example, the answer to log 100 is 2 because 10 to the 2^nd power equals 100.

Logarithm with a different base –Type the base (the small number) inside the brackets and the argument (the regularly sized number) inside parenthesis. For example, would be written as log[2]8. When you change the subscript number on a logarithm, you are changing the base. This example is asking the following: 2 to what power equals 8? The answer: 3.

Note: If no subscript (base) is given, the base is assumed to be 10.

Greater than or equal to – If you need to use just the greater than sign ( > ), simply type it using your keyboard. (Hit shift then the period.)

Less than or equal to – If you need to use just the less than sign ( < ), simply type it using your keyboard. (Hit shift then the comma.)

Division sign –For multiplication, use the asterisk button on your keyboard. (Hit shift then 8.)

Pi – Pi is a unique number that describes the relationship between the circumference and the diameter of every circle. Pi is approximately equal to 3.14.

Union – Union indicates all the values put together. For example, let’s take the union of the following two sets of numbers. Set one is the numbers 1 – 10 and set two is the numbers 5 – 20. The union of the two sets would be all of the numbers put together – so the answer would be numbers 1 – 20. Numbers only have to be in at least one of the sets to be part of the solution.

Intersection –Intersection indicates values that are part of both sets. For example, let’s take the intersection of the following two sets of numbers. Set one is the numbers 1 – 10 and set two is the numbers 5 – 20. The intersection of the two sets would be all of the numbers that are in both sets – so the answer would be numbers 5 – 10. Numbers have to be in both of the sets to be part of the solution.

Practice a little bit every day

Don’t wait to cram the night before a big test – you’ll be overwhelmed and you won’t remember as much. Instead, practice a little bit each night. You’ll find that when test time comes around, you already know most of the material and just need to review. Talk about relieving stress!

Write down questions for your teacher

As you practice, write down any questions to which you can’t find the answer and ask your teacher about it the next day in class. Having a written-down question will help you remember exactly what you wanted to ask and will also help your teacher to be able to answer your question quickly.

Algebra Imath Problem Solving Problems

Work with a friend

Practice problems with a friend so that you can help correct each other’s mistakes. It also makes learning a lot more fun when you’re working together – just make sure you don’t get distracted.

Find your mistakes

Free Algebra Word Problem Solver

When you get a problem wrong, don’t just say “oh well” and try another one. The key to becoming proficient in math is finding and learning from your mistakes. If you don’t figure out what you did wrong, you will likely continue to make the same error. If you can’t find your mistake on your own, ask a friend, teacher, or parent for help. Or, sign up for Mathway – this will show you step-by-step how to work the problem correctly so that you can figure out where you went wrong.