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

1 Answer
Aug 17, 2017

Answer:

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#