Answer
$(-\infty ,-\frac{14}{3}] \cup[2,\infty)$.
Work Step by Step
The given expression is
$\left | 3x+4 \right |\geq10$
Remove the absolute value bars.
$3x+4 \leq -10$ or $3x+4 \geq10$
Subtract $4$ from both sides.
$3x+4-4 \leq -10-4$ or $3x+4-4 \geq10-4$
Simplify.
$3x \leq -14$ or $3x \geq6$
Divide both sides by $3$.
$\frac{3x}{3} \leq \frac{-14}{3}$ or $\frac{3x}{3} \geq \frac{6}{3}$
Simplify.
$x \leq -\frac{14}{3}$ or $x \geq 2$
The solution set is
$(-\infty ,-\frac{14}{3}] \cup[2,\infty)$.
