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 $112^{\text {th }}$ block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?
$|x-112|=0$
$|x-112|=4$
$|4-112|=x$
$|112-4|=x$
Answer (1)
Define x as the turtle's block number.
Express the distance between the turtle and Sharon as ∣ x − 112∣ .
Set the distance equal to the farthest distance the turtle could have gone: ∣ x − 112∣ = 4 .
The equation representing the turtle's possible locations is ∣ x − 112∣ = 4 .
Explanation
Understanding the Problem Let x be the block number where the turtle is. The turtle can be 4 blocks away from Sharon's house in either direction. Sharon lives on the 112th block.
Setting up the Distance The distance between the turtle and Sharon's house is the absolute value of the difference between their block numbers, which is ∣ x − 112∣ .
Forming the Equation Since the farthest the turtle could have gone is 4 blocks, we set the distance equal to 4: ∣ x − 112∣ = 4
Final Answer Therefore, the equation that can be used to find the block numbers that represent the farthest distance that the turtle may be is ∣ x − 112∣ = 4 .
Examples
Imagine you're planning a meeting point with a friend. You know they live 10 blocks away from the center of town. This problem is similar to figuring out the possible locations of your friend, which could be 10 blocks east or west of the center. Understanding absolute value equations helps in scenarios like determining distances, setting boundaries, or planning locations within a certain range.
