How do you solve #7|x+2|=49#?

1 Answer
smendyka
Jan 4, 2017

Isolate the absolute value term and then solve for + and - of what it is equal to. See Explanation for full detailed process.

Explanation:

First step is to isolate the absolute value term by dividing each side of the equation by #color(red)(7)# which will also keep the equation balanced.

#(7abs(x + 2))/color(red)(7) = 49/color(red)(7)#

#(color(red)(cancel(color(black)(7)))abs(x + 2))/cancel(color(red)(7)) = 7#

#abs(x + 2) = 7#

Because the absolute value function transforms a negative or positive term into a positive term we must solve for the term in the absolute value function for both its positive and negative equivalent.

Solution 1)

#x + 2 = 7#

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

#x + 0 = 5#

#x = 5#

Solution 2)

#x + 2 = -7#

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

#x + 0 = -9#

#x = -9#

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