Solve 2x-5/7geq-1

$$2 x - \frac { 5 } { 7 } \geq - 1$$

Solve for x

$$x\geq -\frac{1}{7}$$

Solution Steps

Add \frac{5}{7} to both sides.

$$2x\geq -1+\frac{5}{7}$$

Convert -1 to fraction -\frac{7}{7}.

$$2x\geq -\frac{7}{7}+\frac{5}{7}$$

Since -\frac{7}{7} and \frac{5}{7} have the same denominator, add them by adding their numerators.

$$2x\geq \frac{-7+5}{7}$$

Add -7 and 5 to get -2.

$$2x\geq -\frac{2}{7}$$

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

$$x\geq \frac{-\frac{2}{7}}{2}$$

Express \frac{-\frac{2}{7}}{2} as a single fraction.

$$x\geq \frac{-2}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$x\geq \frac{-2}{14}$$

Reduce the fraction \frac{-2}{14} to lowest terms by extracting and canceling out 2.

$$x\geq -\frac{1}{7}$$