How do you solve #|x - 2| + 5= 7#?

1 Answer
smendyka
Dec 27, 2016

#x = 4# and #x = 0#

Explanation:

The first step is to isolate the absolute value term on one side of the equation:

#abs(x - 2) + 5 - color(red)(5) = 7 - color(red)(5)#

#abs(x - 2) + 0 = 2#

#abs(x - 2) = 2#

Solving for the absolute value is a special situation. The absolute value function takes a positive or a negative term and transforms it to its positive form.

Therefore, we need to solve the term within the absolute value for both the negative and positive term it is equated to.

Solution 1)

#x - 2 = 2#

#x - 2 + color(red)(2) = 2 + color(red)(2)#

#x - 0 = 4#

#x = 4#

Solution 2)

#x - 2 = -2#

#x - 2 + color(red)(2) = -2 + color(red)(2)#

#x - 0 = 0#

#x = 0#

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