Solve 1/2(1/2-2x)leq1/4

$$\frac { 1 } { 2 } ( \frac { 1 } { 2 } - 2 x ) \leq \frac { 1 } { 4 }$$

Solve for x

$$x\geq 0$$

Solution Steps

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$\frac{1}{2}-2x\leq \frac{1}{4}\times 2$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{1}{2}-2x\leq \frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Subtract \frac{1}{2} from both sides.

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

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$-2x\leq 0$$

Product of two numbers is ≤0 if one is ≥0 and the other is ≤0. Since -2\leq 0, x must be ≥0.

$$x\geq 0$$