Answer
The solution is $(-\infty,-3]\cap(-\infty,0]$
Work Step by Step
$4x+2\le-10$ and $2x\le0$
Solve both inequalities separately:
$4x+2\le-10$
Take $2$ to the right side:
$4x\le-10-2$
$4x\le-12$
Take $4$ to divide the right side:
$x\le-\dfrac{12}{4}$
$x\le-3$
The solution is $(-\infty,-3]$
$2x\le0$
Take $2$ to divide the right side:
$x\le\dfrac{0}{2}$
$x\le0$
The solution is $(-\infty,0]$
Since the compound inequality has the word "and", the solution is the intersection of the two solution sets found.
The solution is $(-\infty,-3]\cap(-\infty,0]$
