How do you solve abs(-9+v)/8=3?

1 Answer
smendyka
Aug 17, 2017

See a solution process below:

Explanation:

First, multiply each side of the equation by color(red)(8) to isolate the absolute value function while keeping the equation balanced:

color(red)(8) xx abs(-9 + v)/8 = color(red)(8) xx 3

cancel(color(red)(8)) xx abs(-9 + v)/color(red)(cancel(color(black)(8))) = 24

abs(-9 + v) = 24

The absolute value function takes any negative or positive 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:

-9 + v = -24

color(red)(9) - 9 + v = color(red)(9) - 24

0 + v = -15

v = -15

Solution 2:

-9 + v = 24

color(red)(9) - 9 + v = color(red)(9) + 24

0 + v = 33

v = 33

The Solutions Are: v = -15 and v = 33

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