How do you solve #2| x + 7| - 4= 6#?

1 Answer
smendyka
Dec 5, 2016

#x = -2# and #x = -12#

Explanation:

The first step to solving an absolute value equation is to isolate the absolute value term on one side of the equation while keeping the equation balanced:

#2abs(x + 7) - 4 + 4 = 6 + 4#

#2abs(x + 7) = 10#

#(2abs(x + 7))/2 = 10/2#

#abs(x + 7) = 5#

The next step is to solve for the postive and negative of the solution because the absolute value turn with take either positive or negative numbers and transform them into positive numbers.

#x + 7 = 5#

#x + 7 - 7 = 5 - 7#

#x = -2#

and

#x + 7 = -5#

#x + 7 - 7 = -5 - 7#

#x = -12#

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