Answer
$-6, \frac{4}{3}$.
Work Step by Step
Step 1. Remove the absolute sign to get two cases: $2x+1=5-x$ and $2x+1=-(5-x)=-5+x$
Step 2. For $2x+1=5-x$, we have $3x=4$ thus $x=\frac{4}{3}$
Step 3. For $2x+1=-5+x$, we have $x=-6$
Step 4. The solutions are $x=-6$ and $x=\frac{4}{3}$.
