How do you solve #|9 - 3g| <= 12#?

1 Answer
Trevor Ryan.
Feb 21, 2016

#g in [-1,7]#

Explanation:

By definition of absolute value functions, we may write this as

#-12<=9-3g<=12#

Now subtract #9# throughout to yield

#-21<=-3g<=3#

Now divide by #-3# throughout to obtain the solution, bearing in mind that when an inequality is multiplied or divided by a negative number, its sign changes around.

#7>=g>=-1#

In interval notation, this becomes

#g in [-1,7]#

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