Answer
$-\frac{5}{2}, 1$ .
Work Step by Step
Step 1. Remove the absolute sign to get two cases: $4x+3=7$ and $4x+3=-7$
Step 2. For $4x+3=7$, we have $4x=4$ thus $x=1$
Step 3. For $4x+3=-7$, we have $4x=-10$ thus $x=-\frac{5}{2}$
Step 4. The solutions are $x=-\frac{5}{2}$ and $x=1$ .
