How do you solve # 3 abs(5g+2) -8 ≥ 7# and find any extraneous solutions?

1 Answer
Parabola
Dec 15, 2017

This inequality will hold true if the #g# values are greater than or equal to #3/5#, or less than or equal to #-7/5# The solution is not extraneous.

Explanation:

First, we isolate #abs(5g+2)#
#3abs(5g+2)-8>=7#
#3abs(5g+2)>=15#
#abs(5g+2)>=5#

Since the variable side is larger than the number side, we know this is a disjunction. Therefore, we write down the two possibilities.
#5g+2>=5#
#5g+2<=-5#

Solve each one.
#5g+2>=5#
#5g>=3#
#g>=3/5#

#5g+2<=-5#
#5g<=-7#
#g<=-7/5#

This means that this inequality will hold true if the #g# values are greater than or equal to #3/5# ,or less than or equal to #-7/5# These values are not extraneous, since they use "or" between the two different situations instead of "and". If this somehow were a conjunction, this would have been extraneous.

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