Solve the problem.
-A real estate development consists of home sites that range in width from 53 to 119 feet and in depth from 140 to 194 feet. Using $x$ as the variable in both cases, write absolute value inequalities that correspond to these ranges.
A) $| x - 86 | \leq 33 , | x - 167 | \leq 27$
B) $| x - 33 | \leq 86 , | x - 27 | \leq 167$
C) $| B - 66 | \leq 53 , | x - 54 | \leq 140$
D) $| B - 53 | \leq 66 , | x - 140 | \leq 54$

Question

Quizplus · Accepted Answer

The correct absolute value inequalities are found by taking the average of the minimum and maximum values for width and depth, then finding the difference between the average and either extreme. For width: average = $\frac{53 + 119}{2} = 86$, difference = $119 - 86 = 33$, so $| x - 86 | \leq 33$. For depth: average = $\frac{140 + 194}{2} = 167$, difference = $194 - 167 = 27$, so $| x - 167 | \leq 27$.

Solve the Problem xxx As the Variable in Both Cases, Write Absolute Value Inequalities

Solve the Problem $x$ As the Variable in Both Cases, Write Absolute Value Inequalities