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

1 Answer
Sep 3, 2016

Answer:

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 xx 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.

# {+ ( 7p + 4) /8} xx 8 = 3 xx 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

# 7p/7# = # 20/7# This gives p = # 20/7#

Now take the negative value of the absolute value term.

# { -( 7p +4) / 8) xx 8 = 3 xx 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 p/-7 = 28/-7# This gives

p = -4