Question

The average body temperature of a lemming is 98.6 degrees Fahrenheit. The

temperature is considered abnormal if it is more than 1.5 degrees above or below that.
Write the absolute value inequality that represents this.

Answer 1

`|x - 98.6| > 1.5`

Explanation:

Given

Temperature = 98.6F

Range = 1.5F

Required

Write the absolute value inequality

Let the temperature be represented by x

We start by writing an expression for the difference between x and 98.6.

This can be written as x - 98.6

From the question, we understand that this difference is more than 1.5F

Representing this using absolute value inequality; we have

`|x - 98.6| > 1.5`

Solving further; this gives

`x - 98.6 > 1.5` or
`x - 98.6 < -1.5`

Make x the subject of formula in both cases

`x >98.6 +1.5` or
`x < 98.6-1.5`

`x >100.1` or
`x < 97.1`

This can be rewritten as

`x >100.1` or
`97.1>x`

Combining these two inequalities;

`97.1 > x > 100.1`

Hence;

The absolute inequality is
`|x - 98.6| > 1.5`

And the range of value is
`97.1 > x > 100.1`