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]}

How do you solve the absolute value of equation 3abs(2a+7)+6=3a+183abs(2a+7)+6=3a+18?