Question

solve for all values of b in simplest form.
21 = |5 - 4b|
answer

Explanation:

Step1: Split absolute value equation

Set up two cases: $5-4b=21$ and $5-4b=-21$

Step2: Solve first case for b

Subtract 5, then divide by -4:
$5-4b=21 \\
-4b=21-5 \\
-4b=16 \\
b=\frac{16}{-4}=-4$

Step3: Solve second case for b

Subtract 5, then divide by -4:
$5-4b=-21 \\
-4b=-21-5 \\
-4b=-26 \\
b=\frac{-26}{-4}=\frac{13}{2}$

Answer:

$b=-4$ and $b=\frac{13}{2}$