The solution of the absolute value equation is x = 12, and the extraneous solution is x = -4
How to solve the absolute value equation?
Here we have the equation:
|6x + 72| = 12*x
Then we can rewrite this in two ways as:
6x + 72 = -12*x
6x + 72 = 12x
We can find two solutions for x. For the first one:
6x + 12x + 72 = 0
18x = -72
x = -72/18 = -4
For the other equation we get:
6x - 12x + 72 = 0
6x = 72
x = 72/6 = 12
Which is the extraneous solution?
It is x = -4, because we will get:
|6*-4 + 72| = 12*-4
48 = -48
If you want to learn more about absolute values:
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