Question

Solve and graph the inequality

Answer 1

The graph in the attached figure

Explanation:

we have

`\left|x\right|<18`

we know that

The absolute value function has two solutions

case positive

`+(x)<18`

The solution is the interval------> (-∞,18)

All real numbers less than 18

In a number line is the shaded area to the left at point x=18 (open circle)

case negative

`-(x)<18`

Multiply by -1 both sides

`(x)>-18`

The solution is the interval------> (-18,∞)

All real numbers greater than -18

In a number line is the shaded area to the right at point x=-18 (open circle)

therefore

The solution of the inequality

`\left|x\right|<18`

All real numbers greater than -18 and less than 18

see the attached figure to better understand the problem