#### Answer

The solution is $(-\infty,-4]\cup[-1,\infty)$

#### Work Step by Step

$|2x+5|\ge3$
Solving this absolute value inequality is equivalent to solving two separate inequalities, which are:
$2x+5\ge3$ and $2x+5\le-3$
$\textbf{Solve the first inequality:}$
$2x+5\ge3$
Take $5$ to the right side:
$2x\ge3-5$
$2x\ge-2$
Take $2$ to divide the right side:
$x\ge-\dfrac{2}{2}$
$x\ge-1$
$\textbf{Solve the second inequality:}$
$2x+5\le-3$
Take $5$ to the right side:
$2x\le-3-5$
$2x\le-8$
Take $2$ to divide the right side:
$x\le-\dfrac{8}{2}$
$x\le-4$
Expressing the solution in interval notation:
$(-\infty,-4]\cup[-1,\infty)$