Answer
$b = 13, -27$
Work Step by Step
$| b + 7 | = 20$
$b = 20 - 7$
$b = 13$
$-(b + 7) = 20$
$-b - 7 = 20$
$-b = 20 + 7$
$-b = 27$
$b = -27$
Check:
When $b = 13$
$| 13 + 7 | \overset{?}{=} 20$
$20 = 20$
When $b = -27$
$| -27 + 7 | \overset{?}{=} 20$
$| - 20 | \overset{?}{=} 20$
$20 = 20$
