How do you solve #abs(x/7)=3#?

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Answer 1 · 2017-06-12T03:43:36

#x=+-21#

Solve:

#abs(x/7)=3#

#absa=+-a# There are two equations to solve: one is positive, the other is negative.

Positive equation.

#x/7=3#

Multiply both sides by #7#.

#color(red)cancel(color(black)(7))xx x/color(red)cancel(color(black)(7))=3xx7#

#x=21#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Negative equation.

#-x/7=3#

Multiply both sides by #7#.

#-x=3xx7#

#-x=21#

Divide both sides by #-1#.

#(color(red)cancel(color(black)(-))x)/(color(red)cancel(color(black)(-))1)=21/(-1)#

#x=-21#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solution:

#x=+-21#