Solve (3x-1)^2>1

$$( 3 x - 1 ) ^ { 2 } > 1$$

Solve for x

$$x\in \left(-\infty,0\right)\cup \left(\frac{2}{3},\infty\right)$$

Solution Steps

Factor out x.

$$3x\left(3x-2\right)>0$$

For the product to be positive, x and x-\frac{2}{3} have to be both negative or both positive. Consider the case when x and x-\frac{2}{3} are both negative.

$$x<0 x-\frac{2}{3}<0$$

The solution satisfying both inequalities is x<0.

$$x<0$$

Consider the case when x and x-\frac{2}{3} are both positive.

$$x-\frac{2}{3}>0 x>0$$

The solution satisfying both inequalities is x>\frac{2}{3}.

$$x>\frac{2}{3}$$

The final solution is the union of the obtained solutions.

$$x<0\text{; }x>\frac{2}{3}$$