Question

Solution of $|x+1|+|2x+3|=5$ is

• A. $\{-2,\frac{1}{2}\}$
• B. $\{-4,\frac{1}{4}\}$
• C. $\{-3,\frac{1}{3}\}$
• D. $\{-1,1\}$

Answer 1

The correct option is C $\{-3,\frac{1}{3}\}$

$|x+1|+|2x+3|=5$
There are three possible cases

Case $1:$ $x<-\frac{3}{2}$, then
$-x-1-2x-3=5$
$\Rightarrow -3x-4=5$
$\Rightarrow -3x=9$
$\Rightarrow x=-3\in (-\infty ,-\frac{3}{2})$

Case $2:$ $-\frac{3}{2}\le x\le -1$, then
$\Rightarrow -x-1+2x+3=5$
$\Rightarrow x+2=5$
$\Rightarrow x=3\notin [-\frac{3}{2},-1]$
So, there is no value of $x$ for Case$-2$

Case $3:$ $x>-1$, then
$x+1+2x+3=5$
$\Rightarrow 3x+4=5$
$\Rightarrow 3x=1$
$\Rightarrow x=\frac{1}{3}\in (-1,\infty )$

Now, Case $\left(1\right)\cup \left(2\right)\cup \left(3\right)$
$x=\{-3,\frac{1}{3}\}$