How do you solve #a-2<3a+2(a+3)#?

1 Answer
Alan P.
Apr 18, 2016

#a > -2#

Explanation:

Given:
#color(white)("XXX")a-2 < 2a+2(a+3)#

Simplify the right side:
#color(white)("XXX")a-2 < 3a +2a+6#

#color(white)("XXX")a-2 < 5a+6#

Subtract #(a+6)# from both sides
#color(white)("XXX")-8 < 4a#

Divide both sides by #4#
#color(white)("XXX")-2 < acolor(white)("XX")orcolor(white)("XX")a > -2#

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Remember:
When working with inequalities you can:
#color(white)("XXX")#add or subtract the same amount to both sides; and
#color(white)("XXX")#multiply or divide both sides by the same positive amount.
without changing the direction of the inequality sign.

If you multiply or divide both sides by an negative amount:
#color(white)("XXX")#the inequality sign must be reversed.

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