#### Answer

$-\frac{1}{2}$ $\leq$ $d$ $\leq$ $\frac{25}{4}$

#### Work Step by Step

$3|d-4$ $\leq$ $13-d$
Divide both sides by $3$
$|d-4|$ $\leq$ $\frac{13}{3}-\frac{1}{3}d$
Rewrite as a compound inequality
$d-4$ $\leq$ $\frac{13}{3}-\frac{1}{3}d$
or
$d-4$ $\geq$ $-\frac{13}{3}+\frac{1}{3}d$
Work through the first equation
$d-4$ $\leq$ $\frac{13}{3}-\frac{1}{3}d$
Add $\frac{1}{3}d$ to both sides
$\frac{4}{3}d-4$ $\leq$ $\frac{13}{3}$
Add $4$ to each side
$\frac{4}{3}d$ $\leq$ $\frac{25}{3}$
Multiply each side by $\frac{3}{4}$
$d$ $\leq$ $\frac{25}{4}$
Now work through the second equation
$d-4$ $\geq$ $-\frac{13}{3}+\frac{1}{3}d$
Subtract $\frac{1}{3}d$ from both sides
$\frac{2}{3}d-4$ $\geq$ $-\frac{13}{3}$
Add $4$ to both sides
$\frac{2}{3}d$ $\geq$ $-\frac{1}{3}$
Multiply each side by $\frac{3}{2}$
$d$ $\geq$ $-\frac{1}{2}$
$-\frac{1}{2}$ $\leq$ $d$ $\leq$ $\frac{25}{4}$