Solve 1/2x-2/5geq3

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

Solve for x

$$x\geq \frac{34}{5}$$

Solution Steps

Add \frac{2}{5} to both sides.

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

Convert 3 to fraction \frac{15}{5}.

$$\frac{1}{2}x\geq \frac{15}{5}+\frac{2}{5}$$

Since \frac{15}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x\geq \frac{15+2}{5}$$

Add 15 and 2 to get 17.

$$\frac{1}{2}x\geq \frac{17}{5}$$

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

$$x\geq \frac{17}{5}\times 2$$

Express \frac{17}{5}\times 2 as a single fraction.

$$x\geq \frac{17\times 2}{5}$$

Multiply 17 and 2 to get 34.

$$x\geq \frac{34}{5}$$