Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$1\le x \le 3$
$\bf{\text{Solution Outline:}}$ 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).