## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 2 - Solving Equations - 2-3 Solving Multi-Step Equations - Practice and Problem-Solving Exercises - Page 98: 18

#### Answer

$a=13$

#### Work Step by Step

This problem deals with combining like terms. Like terms are terms that have the same variable raised to the same power. Note, by this definition, numbers like 10 and 15 are also like terms as they are multiplied by a variable raised to the zeroth power. This concept may seem confusing, but it makes sense if we consider it for a second. Anything raised to the zeroth power is one. Thus, $x^{0}$ is 1. Earlier in the chapter, we learned the Identity Property of Multiplication, which states that anything times one is itself. Thus, 15 is equal to 15$x^{0}$ because $x^{0}$ is equal to 1. Now, back to the problem. Recall, if terms are like terms, we can add or subtract these terms just like we add or subtract numbers. Thus, because -2a and a are like terms, we can add them to simplify the equation to $-a-10=-23$. We now need to get the a alone. Thus, we cancel out the subtraction by adding 10 on both sides. This leaves us with the equation $-a=-13$. In order to cancel out multiplication, we use division, so we divide both sides by -1 to get that $a=13$. We plug 13 in for a and confirm that our answer is, indeed, correct.

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