Question

sharons 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 \\) \\( |4 - 112| = x \\) \\( |x - 112| = 4 \\) \\( |112 - 4| = x \\)

Explanation:

Step1: Understand absolute value meaning

The absolute value \(|a - b|\) represents the distance between \(a\) and \(b\) on the number line. Here, \(x\) is the block number the turtle is on, and \(112\) is Sharon's block. The distance between \(x\) and \(112\) should be at most \(4\) (since the farthest is \(4\) blocks in either direction). So the equation is \(|x - 112| = 4\) (this equation finds the values of \(x\) that are \(4\) units away from \(112\) on the number line, which are the farthest blocks the turtle could be on).

Step2: Analyze other options

• \(|x - 112| = 0\) would mean \(x = 112\), which is Sharon's block, not the farthest.
• \(|4 - 112| = x\) calculates the distance between \(4\) and \(112\), not related to the turtle's possible blocks.
• \(|112 - 4| = x\) also calculates a fixed distance, not the possible blocks of the turtle.

Answer:

\(|x - 112| = 4\)