Answer
$\left [\frac{-13}{3} ,5\right ]$.
Work Step by Step
$\Rightarrow |3x-1|\leq14$
Rewrite the inequality without absolute value bars.
$\Rightarrow -14\leq3x-1\leq14$
Add $1$ to all three parts.
$\Rightarrow -14+1\leq3x-1+1\leq14+1$
Simplify.
$\Rightarrow -13\leq3x\leq15$
Divide all three parts by $3$.
$\Rightarrow \frac{-13}{3}\leq\frac{3x}{3}\leq\frac{15}{3}$
Simplify.
$\Rightarrow \frac{-13}{3}\leq x\leq5$
The interval notation is $\left [\frac{-13}{3} ,5\right ]$.
