Question

The value(s) of $x$ for which $|2x-3|-|x+2|=4$ holds true, is

• A. $\{1,9\}$
• B. $\{-1,9\}$
• C. $\{-1,1\}$
• D. $\left\{9\right\}$

Answer 1

The correct option is B $\{-1,9\}$

$|2x-3|-|x+2|=4$
When $x<-2$
$-x+5=4$
$\Rightarrow x=1$ No solution

When $-2\le x<\frac{3}{2}$
$-3x+1=4$
$\Rightarrow x=-1$

When $x\ge \frac{3}{2}$
$x-5=4$
$\Rightarrow x=9$

$\therefore x=-1,9$