#### Answer

$\left[ 3,5 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
8 \le 3x-1 \lt 14
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Removing the grouping symbols and using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
8+1 \le 3x-1+1 \lt 14+1
\\\\
9 \le 3x \lt 15
\\\\
\dfrac{9}{3} \le \dfrac{3x}{3} \lt \dfrac{15}{3}
\\\\
3 \le x \lt 5
.\end{array}
In interval notation, the solution set is $
\left[ 3,5 \right)
.$