Question

sharon’s turtle escaped from her backyard sometime in the last few hours. according to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. if sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?
○ |x - 112| = 0
○ |x - 112| = 4
○ |4 - 112| = x
○ |112 - 4| = x

Explanation:

Step1: Understand Absolute Value Meaning

The absolute value \(|x - a|\) represents the distance between \(x\) and \(a\) on the number line. Here, \(a = 112\) (Sharon's block), and the distance the turtle can be from her block is 4.

Step2: Match the Equation

We need an equation where the distance between \(x\) (turtle's block) and 112 is 4. So the equation is \(|x - 112| = 4\). Let's check other options:

• \(|x - 112| = 0\) means \(x = 112\), no distance, wrong.
• \(|4 - 112| = x\) calculates \(| - 108| = x\), \(x = 108\), not about distance from 112, wrong.
• \(|112 - 4| = x\) is \(|108| = x\), \(x = 108\), same issue, wrong.

Answer:

B. \(|x - 112| = 4\)