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

1 Answer
smendyka
May 23, 2018

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}

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