Solve x+2/3geq5/6

$$\frac { x + 2 } { 3 } \geq \frac { 5 } { 6 }$$

Solve for x

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

Solution Steps

Multiply both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x+2\geq \frac{5}{6}\times 3$$

Express \frac{5}{6}\times 3 as a single fraction.

$$x+2\geq \frac{5\times 3}{6}$$

Multiply 5 and 3 to get 15.

$$x+2\geq \frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

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

Subtract 2 from both sides.

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

Convert 2 to fraction \frac{4}{2}.

$$x\geq \frac{5}{2}-\frac{4}{2}$$

Since \frac{5}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$x\geq \frac{5-4}{2}$$

Subtract 4 from 5 to get 1.

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