Question

A pedestrian bridge is 53 meters long. Due to changes in temperature, the bridge may expand or contract by as much as 21 millimeters. Write and solve an absolute-value equation to find the minimum and maximum lengths of the bridge.

Answer 1

Length of bridge = 53 meters

Length changes expected due to changes in temperature = expansion or contraction by 21 millimeters (or 0.021 meters)

Let length of bridge at any given time be 'a'

As an absolute value equation, the situation can be expressed as:

⇒ |a-53| < 0.021

Solving the equation

⇒ -0.021 < a-53 < 0.021

⇒ 53 - 0.021 < a < 53 + 0.021

⇒ 52.979 < a < 53.021

Hence, the minimum length of the bridge can be 52.979 meters and the maximum length of the bridge can be 53.021 meters.