Question

Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?

Answer 1

Letting x be the number of the block:

|x-57|=3

This makes the absolute difference between his house and the new block number equal to three.

Answer 2

The correct answer is:

|x - 57| = 3.

Explanation:

Let x be the block Jamaal walks to.  

We know that Jamaal's house is on the 57th block.  We also know that the distance he is allowed to walk is no more than 3 blocks.  To find the distance between his house and the block he walks to, we subtract:

x - 57 = 3

However, Jamaal can walk 3 blocks in any direction from his home.  This means he could walk in a "positive" direction or a "negative" direction; this means we must take the absolute value (absolute value represents distance without regard to number sign):

|x - 57| = 3.