How do you solve #3|x| - 12 = 18#?

1 Answer
sente
Jan 8, 2016

#x = 10# or #x = -10#

Explanation:

Before beginning, note that #|a| = |-a| = a# for any real number #a > 0#.
This matters as it means we can have multiple solutions to the problem. For example, because #|1| = |-1| = 1#,
#|y| = 1# has the solutions #y=1# or #y=-1#.

Now, for the given problem:

#3|x| - 12 = 18#

#=> 3|x| - 12 + 12 = 18 + 12#

#=> 3|x| = 30#

#=> 1/3 * 3|x| = 1/3 * 30#

#=> |x| = 10#

#=> x = 10# or #x = -10#

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