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Combining Like Terms

A Second Equation Example

The next example equation is shown below. Solving this equation will require both Simplifying Multiple Signs and Combining Like Terms.

-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. Review the Simplifying Multiple Signs lesson if this concept is unfamiliar to you. When this step is completed, the equation becomes

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

We will start combining like terms on the left side with -9, a constant. The only other constant on the left side is -10, so we can add the two together as shown below. The sum of -9 and -10 is -19, thus the equation becomes

-19 + 12x - 4x = 8x - 6x + 46 + 1

Next we will add together 12x and -4x because they are like terms (x to the first power is the only variable in each). The resulting equation is shown below:

-19 + 8x = 8x - 6x + 46 + 1

Now that all like terms on the left side have been combined, we start working on the right side by adding the constants 46 and 1 to get 47.

-19 + 8x = 8x - 6x + 46 + 1

Then we add the 8x and -6x to get 2x. The resulting equation is

8x - 19 = 2x + 47

Now, the equation can be solved using addition, subtraction, and division, as presented in the Equation Basics lesson.

Proceed to the next page to find some additional resources including a link to our Equation Calculator which can guide you though similar problems.


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