How do you solve #3|x+11|=24#?

1 Answer
Sep 28, 2017

Answer:

See a solution process below:

Explanation:

First, divide each side of the equation by #color(red)(3)# to isolate the absolute value function while keeping the equation balanced:

#(3abs(x + 11))/color(red)(3) = 24/color(red)(3)#

#(color(red)(cancel(color(black)(3)))abs(x + 11))/cancel(color(red)(3)) = 8#

#abs(x + 11) = 8#

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:

#x + 11 = -8#

#x + 11 - color(red)(11) = -8 - color(red)(11)#

#x + 0 = -19#

#x = -19#

Solution 2:

#x + 11 = 8#

#x + 11 - color(red)(11) = 8 - color(red)(11)#

#x + 0 = -3#

#x = -3#

The Solutions Are: #x = -19# and #x = -3#