Need help finding parameter a of solved equation

[rocketFrog]

Hi all,
I'm stuck solving an equation that states: Solve the equation for x ; (a ∈ R) then find parameter 'a' such that |x| < 1. I had no trouble solving the equation it's self that evaluates to: x = 2a / 3a - 4; but I'm stuck at the second part since I'm not so sure about what I'm supposed to do or how to set up the equation to find parameter a, so I could use an explanation.

I've attached the work I've done so far (solving the equation).

Thanks in advance!

 

[R.M.]

Let x = 1 and solve for a. Let x = -1 and solve for a again. These 2 values of a split a number line into 3 regions. Choose a value from each region to test. Also keep in mind the value of a that makes your denominator equal to 0.

 

[rocketFrog]

Thanks for the help, I appreciate it!
I got:



and that a ≠ 1.333333