How do you solve #abs(3x+4)=20#?

1 Answer
Mar 13, 2018

Answer:

See a solution process below:

Explanation:

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:

#3x + 4 = -20#

#3x + 4 - color(red)(4) = -20 - color(red)(4)#

#3x + 0 = -24#

#3x = -24#

#(3x)/color(red)(3) = -24/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -8#

#x = -8#

Solution 2:

#3x + 4 = 20#

#3x + 4 - color(red)(4) = 20 - color(red)(4)#

#3x + 0 = 16#

#3x = 16#

#(3x)/color(red)(3) = 16/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 16/3#

#x = 16/3#

The Solution Set Is: #x = {-8, 16/3}#