How do you solve the absolute value of equation #3abs(2a+7)+6=3a+18#?

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Answer 1 · 2015-04-02T12:39:23

We first make life a bit easier by dividing everything by #3#:

#|2a+7|+2=a+6->|2a+7|=a+4->#
# |2a+7|-a=4#

(1)
For #a>= - 3 1/2# the absolutes are not necessary:

#2a+7-a=4->a=-3# which is acceptable

(2)
For #a< -3 1/2# the equation is turned around:

#-(2a+7)-a=4->-3a=11->a=-11/3= -3 2/3# which is below #-3 1/2# and so also acceptable

So the solutions are: #a=-3# and #a=-3 2/3#
graph{|2x+7|-x [-12.54, 7.46, 1.16, 11.16]}