How do you solve #4|x + 5| + -6 = 34#?

1 Answer
Apr 19, 2017

Answer:

#x = 5, x = -15#

Explanation:

Given: #4|x+5| + -6 = 34#

Start by adding #6# to both sides of the equation:

#4|x+5| + -6 + 6 = 34 + 6#

Simplify: #4|x+5| = 40#

Divide both sides by #4#: #(4|x+5|)/4 = 40/4#

Simplify: #|x+5| = 10#

Break the function into two equations:
#y = |x+a| " is " y = x +a" and " y = -(x+a)#

#|x+5| = 10 " is " x+5 = 10 " and " -(x+5) = 10#

Solve each equation:

#x+5 = 10#
#x+5 - 5 = 10 - 5#
#x = 5#

#-(x+5) = 10#
# -x - 5 = 10#
# -x -5 + 5 = 10 + 5#
# -x = 15#
# x = -15#

Check answers :
#4|5+5| + -6 = 4*10 -6 = 40 - 6 = 34#
#4|5 + -15| + -6 = 4|-10| - 6 = 4(10) - 6 = 34#