How do you solve abs(7p+4)/8=3?

Sep 3, 2016

p = -4 or p = # 20/7 Make the absolute value term both positive and negative and solve for p

Explanation:

The absolute value term can be either positive or negative in value as long as it equals $8 \times 3$

The goal is to isolate and solve for p so first multiply both sides by 8

First take the positive value of the absolute value term.

$\left\{+ \frac{7 p + 4}{8}\right\} \times 8 = 3 \times 8$ This gives

$$7p + 4  = 24       Subtract 4 from both sides


7p + 4 - 4 = 24 - 4 This gives

7p = 20 Divide both sides by 7

$7 \frac{p}{7}$ = $\frac{20}{7}$ This gives p = $\frac{20}{7}$

Now take the negative value of the absolute value term.

$\left\{- \frac{7 p + 4}{8}\right) \times 8 = 3 \times 8$ This gives

• 7p -4 = 24 add 4 to both sides

• 7p - 4 + 4 = 24 + 4 This gives

-7p = 28 divide both sides by -7

$- 7 \frac{p}{-} 7 = \frac{28}{-} 7$ This gives

p = -4