How do you solve #|x + 5| - 4= 11#?

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Answer 1 · 2016-12-15T18:51:50

#x = 10# and #x = -20#

First, isolate the absolute value term on one side of the equation while keeping the equation balanced:

#abs(x + 5) - 4 + 4 = 11 + 4#

#abs(x + 5) - 0 = 15#

#abs(x + 5) = 15#

Because this is an absolute value question we must solve the interior of the absolute value function for both a positive and negative result:

Solution 1)

#x + 5 = 15#

#x + 5 - 5 = 15 - 5#

#x + 0 = 10#

#x = 10#

Solution 2)

#x + 5 = - 15#

#x + 5 - 5 = -15 - 5#

#x + 0 = -20#

#x = -20#