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Solve for x: 8x - 2 = -9 + 7x.

Question:

Solve for {eq}x {/eq}: {eq}\; 8x - 2 = -9 + 7x {/eq}.

Isolating a Variable

In isolating a variable, the terms beside is when it crosses over the equal sign will change signs. The coefficient of the variable itself has to be divided from both sides of the equation without any change in sign.

Answer and Explanation:

To solve for {eq}x {/eq} from:

{eq}8x - 2 = -9 + 7x {/eq}

We collect like terms:

{eq}8x - 7x = -9 +2 {/eq}

{eq}x = -7 {/eq}

To check, substitute {eq}x = -7 {/eq} in the original equation:

{eq}8x - 2 = -9 + 7x {/eq}

{eq}8(-7) - 2 \stackrel{?}{=} -9 + 7(-7) {/eq}

{eq}-56 - 2 \stackrel{?}{=} -9 - 49 {/eq}

{eq}-58 \stackrel{\checkmark}{=} -58 {/eq}

Thus, the value of {eq}x {/eq} is {eq}-7 {/eq}.


Learn more about this topic:

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Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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