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

Given that a pedestrian bridge has length of 53 meters. and due to change in temperature, bridge may expand or contract by 21 millimeters = $\frac{21}{1000} = 0.021 meters$

Let x be the new length which is contracted or expanded due to temperature change.

So, change in length of bridge due to temperature may be x-53 ( for expansion) or 53-x (for contraction).

But given this change must be 0.021.

Absolute function for change in bridge length = |53-x|

Hence absolute value equation is |53-x| = 0.021

Which means 53-x=0.021    or    53-x = -0.021

                        x=53-0.021     or      x= 53+0.021

                       x=52.979 m or  53.021 meters

Hence minimum and maximum length of the bridge are 52.979 meters and 53.021 meters.