## College Algebra (11th Edition)

$\left( -\infty, -4\right] \cup\left[ -1,\infty \right)$
Since for any $a\gt0$, $|x|\gt a$ implies $x \gt a$ or $x\lt -a$ then the solution to the given inequality, $\left| 2x+5 \right|\ge 3 ,$ is \begin{array}{l}\require{cancel} 2x+5\ge 3 \\\\ 2x\ge 3-5 \\\\ 2x\ge -2 \\\\ x\ge -\dfrac{2}{2} \\\\ x\ge -1 ,\\\\\text{OR}\\\\ 2x+5\le -3 \\\\ 2x\le -3-5 \\\\ 2x\le -8 \\\\ x\le -\dfrac{8}{2} \\\\ x\le -4 .\end{array} Hence, the solution set is the interval $\left( -\infty, -4\right] \cup\left[ -1,\infty \right) .$ Note that the symbol "$>$" may be replaced by "$\ge$".