## College Algebra (11th Edition)

$\left( \dfrac{2}{3}, 2\right)$
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x \lt a$ then the solution to the given inequality, $\left| 3x-4 \right|\lt 2 ,$ is \begin{array}{l}\require{cancel} -2\lt 3x-4\lt 2 \\\\ -2+4\lt 3x-4+4\lt 2+4 \\\\ 2\lt 3x\lt 6 \\\\ \dfrac{2}{3}\lt \dfrac{3x}{3}\lt \dfrac{6}{3} \\\\ \dfrac{2}{3}\lt x\lt 2 .\end{array} Hence, the solution set is the interval $\left( \dfrac{2}{3}, 2\right) .$