Question

For the following exercises, solve each inequality and write the solution in interval notation.

31. | 3x − 4 | ≤ 8

Answer 1

The solution set in interval form is
`$\left[(-4)/(3), 4\right]$`.

Explanation:

It is given in the question an inequality as
`$|3 x-4| \leq 8$`.

It is required to determine the solution of the inequality.

To determine the solution of the inequality, solve the inequality
`$3 x-4 \leq 8$` and,
`$-8 \leq 3 x-4$`.

Step 1 of 2

Solve the inequality
`$3 x-4 \leq 8$`

`$$\begin{aligned}&3 x-4 \leq 8 \\&3 x-4+4 \leq 8+4 \\&3 x \leq 12 \\&x \leq 4\end{aligned}$$`

Solve the inequality
`$-8 \leq 3 x-4$`.

`$$\begin{aligned}&-8+4 \leq 3 x-4+4 \\&-4 \leq 3 x \\&-(4)/(3) \leq x \\&x \geq-(4)/(3)\end{aligned}$$`

Step 2 of 2

The common solution from the above two solutions is x less than 4 and
`$x \geq-(4)/(3)$`. The solution set in terms of interval is
`$\left[(-4)/(3), 4\right]$`.