Answer:
The solution set in interval form is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].
Step-by-step explanation:
It is given in the question an inequality as [tex]$|3 x-4| \leq 8$[/tex].
It is required to determine the solution of the inequality.
To determine the solution of the inequality, solve the inequality [tex]$3 x-4 \leq 8$[/tex] and, [tex]$-8 \leq 3 x-4$[/tex].
Step 1 of 2
Solve the inequality [tex]$3 x-4 \leq 8$[/tex]
[tex]$\begin{aligned}&3 x-4 \leq 8 \\&3 x-4+4 \leq 8+4 \\&3 x \leq 12 \\&x \leq 4\end{aligned}$[/tex]
Solve the inequality [tex]$-8 \leq 3 x-4$[/tex].
[tex]$\begin{aligned}&-8+4 \leq 3 x-4+4 \\&-4 \leq 3 x \\&-\frac{4}{3} \leq x \\&x \geq-\frac{4}{3}\end{aligned}$[/tex]
Step 2 of 2
The common solution from the above two solutions is x less than 4 and [tex]$x \geq-\frac{4}{3}$[/tex]. The solution set in terms of interval is [tex]$\left[\frac{-4}{3}, 4\right]$[/tex].
