Answer
The solution is $\Big(-\infty,\dfrac{2}{3}\Big]\cup\Big[2,\infty\Big)$
Work Step by Step
$|3x-4|\ge2$
Solving this absolute value inequality is equivalent to solving two separate inequalities, which are:
$3x-4\ge2$ and $3x-4\le-2$
$\textbf{Solve the first inequality:}$
$3x-4\ge2$
Take $4$ to the right side:
$3x\ge2+4$
$3x\ge6$
Take $3$ to divide the right side:
$x\ge\dfrac{6}{3}$
$x\ge2$
$\textbf{Solve the second inequality:}$
$3x-4\le-2$
Take $4$ to the right side:
$3x\le-2+4$
$3x\le2$
Take $3$ to divide the right side:
$x\le\dfrac{2}{3}$
$\Big(-\infty,\dfrac{2}{3}\Big]\cup\Big[2,\infty\Big)$
