How do you solve #8|12x + 7| = 80#?

1 Answer
Sep 4, 2017

Answer:

See a solution process below:

Explanation:

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

#(8abs(12x + 7))/color(red)(8) = 80/color(red)(8)#

#(color(red)(cancel(color(black)(8)))abs(12x + 7))/cancel(color(red)(8)) = 10#

#abs(12x + 7) = 10#

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:

#12x + 7 = -10#

#12x + 7 - color(red)(7) = -10 - color(red)(7)#

#12x + 0 = -17#

#12x = -17#

#(12x)/color(red)(12) = -17/color(red)(12)#

#(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = -17/12#

#x = -17/12#

Solution 2:

#12x + 7 = 10#

#12x + 7 - color(red)(7) = 10 - color(red)(7)#

#12x + 0 = 3#

#12x = 3#

#(12x)/color(red)(12) = 3/color(red)(12)#

#(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = 1/4#

#x = 1/4#

The Solutions Are: #x = -17/12# and #x = 1/4#