Answer
$1\le x \le 3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
2\le f(x)\le8
,$ replace $f(x)$ with the given function, $
f(x)=3x-1
.$ Then use the properties of inequality to isolate the variable. Finally, graph the solution set.
$\bf{\text{Solution Details:}}$
Replacing $f(x)$ with the given function, then
\begin{array}{l}\require{cancel}
2\le 3x-1\le8
.\end{array}
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
2\le 3x-1\le8
\\\\
2+1\le 3x-1+1\le8+1
\\\\
3\le 3x\le9
\\\\
\dfrac{3}{3}\le \dfrac{3x}{3}\le\dfrac{9}{3}
\\\\
1\le x \le 3
.\end{array}
The graph includes the points from $1$ (inclusive) to $3$ (inclusive).
