Combining Like Terms is a process used to simplify an expression or an equation using addition and subtraction of the coefficients of terms.

Let's say we are given the equation below. It looks very complicated, but if we look carefully, everything is either a constant (a number), or the variable x with a coefficient (4x).

Introduction

**Combining Like Terms**

The Like Terms in the equation bellow are ones that have the same variable. All constants are Like Terms as well. This means that the 15, 10, 6, and -2 are all one set of Like Terms, and the other is 4x, -3x, 5x, and 3x. To combine them is pretty easy, you just add them together and make sure that they are all on the same side of the equation.

Breaking It Down

The process is still not finished, however. There are still some Like Terms, but they are on opposite sides of the equal sign. Since we can do the same thing to both sides we just subtract 4 from each side and subtract 1x from each side.

25+1x=8x+4

Now that you get the idea of combining Like Terms and know the steps you can try to simplify this equation. Remember add/subtract the Like Terms first on their own sides, then move the variables(x) and constants(a number) to separate sides of the equal sign. After that all you have to do is simply solve the equation.

Try It

Now that you have hopefully succeeded simplifying and solving this equation lets go through its process to see if you understand the steps of combining Like Terms.

Do you get it?

There are other coefficients that can be found in equations that are not Like Terms and cannot be combined with other constants or variables.

Different Kinds Of Like Terms

15+4x+10-3x=5x+6+3x-2

15+4x+10-3x=5x+6+3x-2

25+1x=8x+4

7x=21

Now it's just a simple process of dividing by seven on each side.

x=3

-9 + 12x - 10 - 4x = 8x - 6x + 46 - (-1)

-9 + 12x - 10 - 4x = 8x - 6x + 46 - (-1)

The first step to simplifying this equation is to simplify the double negative sign in front of the 1. The second negative sign cancels out the first one, so there are no signs left, meaning that the 1 is positive.

-9 + 12x - 10 - 4x = 8x - 6x + 46 + 1

-19 + 12x - 4x = 8x - 6x + 47

Next you should have added together 12x and -4x because they are Like Terms (x to the first power is the only variable in each) and apply this step to the other side as well with 8x and - 6x.

8x - 19 = 2x + 47

Now all you had to do was move each Like Term to separate sides using adding or subtracting(In this case adding 19 to both sides and subtracting 2x) to completely simplify the equation. Then it would be easy to solve for the solution.

6x = 66

x = 11

5x + y = 4x + 3y

x = 2y

12+17x+2x = 5x -4

2x - 12x +16

Or

Common mistakes can be made with combining different Like Terms such as x & x squared and y & x variables.

People sometimes forget they are not Like Terms and think they can still be added or subtracted together. But you can't because they have different values.

5x + y = 4x + 3y

= xy

6xy = 7xy

Or

12+17x+2x = 5x -4

12 + 19x = 5x - 4

= 14x + 16

I hope you now understand the procedure of combining Like Terms and can perform it correctly.

x-2y

Thank you for watching

:)

Lets just quickly try solving the expressions with x squared and y variables below by how you've been shown correctly.

x -4x -27

6x -14 = 5x +4x + 13

Now we'll go over the correct steps to solve the first given equation.

6x -14 = 5x +4x + 13

You should have started looking for Like Terms to find on each side but in this set equation the Like Terms are on separate sides. Therefore you must have then moved your equation around by putting them in front of the equal sign.

And even though you still haven't solved the equation you have simplified it down enough to be solved using a different method.

3xy + 4xy = 2xy

Now with this expression you had to remember that xy and xy squared do not hold the same values and cannot be combined.

3xy + 4xy = 2xy

All you had to do was add the Like Terms 3xy squared and 4xy squared, then move over the separate 2xy to the same side of the equation with the newly combined Like Terms to fully succeed in simplifying this expression.

7xy - 2xy

By Chloe Sanders

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Citations:

http://www.freemathhelp.com/combining-like-terms.html

http://www.algebrahelp.com/lessons/simplifying/combiningliketerms/pg3.htm

http://www.mathsisfun.com/algebra/like-terms.html

3x + 2x = 10

5x = 10

x = 2

Quiz Questions

-20x+x-12+3y-6-7x

http://www.thatquiz.org/tq/previewtest?V/O/Y/J/45561380207471

3k(1 + 2k) = 2k(5k - 6)

-a(2a + 1) + a(7 = 4a)

http://www.freemathpracticetest.com/printable-math-tests/algebra/algebra0007e.pdf