Answer
If $~~\vert x+3 \vert \lt \frac{1}{2}~~$ then $~~\vert 4x+13 \vert \lt 3$
Work Step by Step
Suppose that $\vert x+3 \vert \lt \frac{1}{2}$
Then:
$\vert x+3 \vert \lt \frac{1}{2}$
$-\frac{1}{2} \lt x+3 \lt \frac{1}{2}$
$-2 \lt 4x+12 \lt 2$
$-1 \lt 4x+13 \lt 3$
$-3 \lt -1 \lt 4x+13 \lt 3$
$\vert 4x+13 \vert \lt 3$
