What sets this problem apart from the more basic absolute value equations is that the absolute value of x equals an expression in terms of x.

This is significant because after you solve the equation, you must check your solutions to ensure that the expression on the other side of the absolute value is in fact a positive value.

In this case:

|x| = 3x - 2

x = 3x - 2
2 = 2x
x = 1

This is a solution -- substitute into the original equation to see that. Now, the "other half" of the process is:

x = -3x + 2
4x = 2
x = 1/2

Now, if you plug this into the right-hand side of the original equation, you get a negative number. This is not a solution, therefore, because |x| must yield a positive number. So (2) is in fact sufficient.

Rey

Hi Ian,
I know trick here is to put back and check your answer, will the distance on number line approach will allow me with this trap? how?

I will IM Ian to help us solve this problem using the distance method.

-V

Thanks Ian
-V