## Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole

# Chapter 2 - Systems of Linear Equations and Inequalities - 2.5 Absolute Value Equations and Inequalities - 2.5 Exercises: 11

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Isolate first the absolute value expression in the givecn equation, $|g-9|+12=8 .$ Then use the definition of absolute value to analyze the solution. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} |g-9|+12=8 \\\\ |g-9|=8-12 \\\\ |g-9|=-4 .\end{array} The absolute value of $x,$ given as $|x|,$ is the distance of $x$ from $0.$ Hence, it is a nonnegative number. In the same way, the left side of the equation above is always a nonnegative number. This will never be equal to the negative number at the right side. Hence, there is $\text{ no solution .}$

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