Question

If $|2x+3|\le 9$ and $2x+3<0$, then

• A. $x\ge -6$
• B. $x<-\frac{3}{2}$
• C. $x\le 3$
• D. $-6\le x\le 3$
• E. $-6\le x\le -\frac{3}{2}$

Answer 1

The correct option is E $-6\le x\le -\frac{3}{2}$

If $|2x+3|\le 9$ and $2x+3<0$

we know that $|x|\to x$ if $x\ge 0$

$x\to -x$ if $x<0$

so, $-(2x+3)\le 9$ and $2x<-3$

$-2x-3-9\le 0$ and $x<-\frac{3}{2}$

$-2x-12\le 0$

$-2(x+6)\le 0$

$x+6\ge 0$ Inequality sign will change here because we multiplying by $(-2)$ both side

$x\ge -6$

Now if we combine both inequalities, on number line then

So, the common part is the correct answer.

So, $-6\le x<-\frac{3}{2}$.