Question

$4|6+2x|-27\le -3$ which of the following best describes the solutions to the inequality shown above ?

• A. $-24\le x\le 0$
• B. $-6\le x\le 0$
• C. $x\le 0orx\ge 3$
• D. No solution

Answer 1

The correct option is B $-6\le x\le 0$

First, isolate the absolute value on the left hand side.
$4|6+2x|-27+27\le -3+27$
$\frac{4|6+2x|}{4}\le \frac{24}{4}$
$|6+2x|\le 6$
Now rewrite this as 2 inequalities without the absolute value
$\begin{array}{c}1):6+2x\le 6\\ 6+2x-6\le 6-6\\ 2x\le 0\\ x\le 0\\ \\ \\ x\le 0\end{array}|\begin{array}{c}2):(6+2x)\le 6\\ -6-2x\le 6\\ add6onbothside\\ -2x\le 12\\ divideby-2\\ -\frac{2x}{-2}\ge \frac{12}{-2}\\ x\ge -6\end{array}$
The following best describes the solution to the inequality
$x\ge -6$ and $x\le 0$
$-6\le x\le 0$