Solve 1/2x+1/2leq3/5

$$\frac { 1 } { 2 } x + \frac { 1 } { 2 } \leq \frac { 3 } { 5 }$$

Solve for x

$$x\leq \frac{1}{5}$$

Solution Steps

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

$$\frac{1}{2}x\leq \frac{3}{5}-\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{1}{2}x\leq \frac{6}{10}-\frac{5}{10}$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x\leq \frac{6-5}{10}$$

Subtract 5 from 6 to get 1.

$$\frac{1}{2}x\leq \frac{1}{10}$$

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

$$x\leq \frac{1}{10}\times 2$$

Multiply \frac{1}{10} and 2 to get \frac{2}{10}.

$$x\leq \frac{2}{10}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$x\leq \frac{1}{5}$$