How do you solve #|5x + 11| = 6#?

1 Answer
Oct 9, 2017

Answer:

See a solution process below: #x = -17/5# and #x = -1#

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:

#5x + 11 = -6#

#5x + 11 - color(red)(11) = -6 - color(red)(11) #

#5x + 0 = -17#

#5x = -17#

#(5x)/color(red)(5) = -17/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -17/5#

#x = -17/5#

Solution 2:

#5x + 11 = 6#

#5x + 11 - color(red)(11) = 6 - color(red)(11) #

#5x + 0 = -5#

#5x = -5#

#(5x)/color(red)(5) = -5/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -1#

#x = -1#

The Solutions Are: #x = -17/5# and #x = -1#