Question

At a trout farm, most of the trout have a length of 23.5 cm. The length of some differ from this by as much as 2.1 cm. Write and solve an absolute-value inequality to find the range of lengths of the trout.

Answer 1

21.4 ≤ x ≤ 25.6

Explanation:

The absolute value of a number is the non-negative value of the number without regard to its sign.

The absolute value of a real number x (|x|) is x for x is positive and -x for x is negative.

Let x represent the length of the trout. Since most trout have a length of 23.5 cm and differ by 2.1 cm, then x can be represented by:

|x - 23.5| ≤ 2.1

x - 23.5 ≤ 2.1 or -(x - 23.5) ≤ 2.1

x ≤ 2.1 + 23.5 or x - 23.5 ≥ -2.1

x ≤ 25.6 or x ≥ 21.4

Hence, the range of lengths of the trout is 21.4 ≤ x ≤ 25.6