Answer
$\left( -\infty, -4\right] \cup\left[ -1,\infty \right)$
Work Step by Step
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 "$\ge$".
