Solve (2x-1)^2/2x-1leq0

$$\frac { ( 2 x - 1 ) ^ { 2 } } { 2 x - 1 } \leq 0$$

Solve for x

$$x<\frac{1}{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\left(2x-1\right)^{1}\leq 0$$

Calculate 2x-1 to the power of 1 and get 2x-1.

$$2x-1\leq 0$$

Add 1 to both sides. Anything plus zero gives itself.

$$2x\leq 1$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x\leq \frac{1}{2}$$