Write the statement as an absolute value inequality.
-A real estate development consists of home sites that range in width from 53 to 105 feet and in depth from 125 to 187 feet. Using $ x $ as the variable in both cases, write absolute value inequalities that correspond to these ranges.
A) $ |x-79| \leq 26,|x-156| \leq 31 $
B) $ |B-52| \leq 53,|x-62| \leq 125 $
C) $ |B-53| \leq 52,|x-125| \leq 62 $
D) $ |x-26| \leq 79,|x-31| \leq 156 $

Question

Quizplus · Accepted Answer

The midpoint of the width range is $\frac{53 + 105}{2} = 79$ and the difference from the midpoint to either end is $105 - 79 = 26$, so $|x - 79| \leq 26$. For depth, the midpoint is $\frac{125 + 187}{2} = 156$ and the difference to either end is $187 - 156 = 31$, so $|x - 156| \leq 31$.

Write the Statement as an Absolute Value Inequality x x x

Write the Statement as an Absolute Value Inequality $x$