Answer
$(-∞,∞)$
Work Step by Step
We are given that $-2x-5\lt-3$ or $6x\lt0$. Therefore, any solutions must only satisfy at least one of the inequalities.
We can first solve $-2x-5\lt-3$
Add 5 to both sides.
$-2x\lt2$
Divide both sides by -2 (which will reverse the inequality sign)
$x\gt-1$
Next, we can solve $6x\lt0$
Divide both sides by 6.
$x\lt0$
Therefore, the solution set consists of all numbers that are greater than -1 or less than 0, which is the set of all real numbers.
