Answer
The solution is $\Big(\dfrac{2}{3},2\Big)$
Work Step by Step
$|3x-4|\lt2$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-2\lt3x-4\lt2$
$\textbf{Solve the inequality shown above:}$
$-2\lt3x-4\lt2$
Add $4$ to all three parts of the inequality:
$-2+4\lt3x-4+4\lt2+4$
$2\lt3x\lt6$
Divide all three parts of the inequality by $3$:
$\dfrac{2}{3}\lt\dfrac{3x}{3}\lt\dfrac{6}{3}$
$\dfrac{2}{3}\lt x\lt2$
Expressing the solution in interval notation:
$\Big(\dfrac{2}{3},2\Big)$
