# Chapter 1 - Section 1.8 - Absolute Value Equations and Inequalities - 1.8 Exercises: 54

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $|-5x+7|-4\lt-6 ,$ use the properties of inequality to isolate the absolute value expression. Then analyze the resulting inequality. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the statement above is equivalent to \begin{array}{l}\require{cancel} |-5x+7|\lt-6+4 \\\\ |-5x+7|\lt-2 .\end{array} The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from $0,$ and hence is always a nonnegative number. In the same way, for any $x$, the expression at the left side is always a nonnegative number. This will never be $\text{ less than }$ the expression at the right. Hence, there is $\text{ no solution .}$

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