How do you solve #abs(v+8)-5=2#?

1 Answer
May 23, 2018

Answer:

See a solution process below:

Explanation:

First, add #color(red)(5)# to each side of the equation to isolate the absolute value function while keeping the equation balanced:

#abs(v + 8) - 5 + color(red)(5) = 2 + color(red)(5)#

#abs(v + 8) - 0 = 7#

#abs(v + 8) = 7#

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

  • Solution 1:

#v + 8 = -7#

#v + 8 - color(red)(8) = -7 - color(red)(8)#

#v + 0 = -15#

#v = -15#

  • Solution 2:

#v + 8 = 7#

#v + 8 - color(red)(8) = 7 - color(red)(8)#

#v + 0 = -1#

#v = -1#

The Solution Set Is: #v = {-15, -1}#