Question

Choosing the absolute value equation that represents a scenario: 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?

Options:
a. |x – 57| = 0
b. |57 – 3| = x
c. |3 – 57| = x
d. |x – 57| = 3

Answer 1

The absolute value equation that represents the scenario where Jamaal is allowed to walk up to three blocks in either direction from his house on the 57th block is |x - 57| = 3.

Step-by-step explanation:

The scenario describes Jamaal who is allowed to walk a distance of three blocks in either direction from his house which is on the 57th block. To represent this situation with an absolute value equation, we look for an equation that allows us to calculate the farthest block Jamaal can walk to while keeping within the three-block limit.

The correct absolute value equation which represents this scenario is |x - 57| = 3. This equation states that the distance (absolute value) between Jamaal's location x and his house at block 57 must be less than or equal to 3 blocks.

Thus, whether Jamaal walks 3 blocks east (toward the higher numbered blocks) or 3 blocks west (toward the lower numbered blocks), the absolute difference from his starting point will be 3, which is within his allowed limit.