Solve 6x+5/7>4x+7

$$6 x + \frac { 5 } { 7 } > 4 x + 7$$

Solve for x

$$x>\frac{22}{7}$$

Solution Steps

Subtract 4x from both sides.

$$6x+\frac{5}{7}-4x>7$$

Combine 6x and -4x to get 2x.

$$2x+\frac{5}{7}>7$$

Subtract \frac{5}{7} from both sides.

$$2x>7-\frac{5}{7}$$

Convert 7 to fraction \frac{49}{7}.

$$2x>\frac{49}{7}-\frac{5}{7}$$

Since \frac{49}{7} and \frac{5}{7} have the same denominator, subtract them by subtracting their numerators.

$$2x>\frac{49-5}{7}$$

Subtract 5 from 49 to get 44.

$$2x>\frac{44}{7}$$

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

$$x>\frac{\frac{44}{7}}{2}$$

Express \frac{\frac{44}{7}}{2} as a single fraction.

$$x>\frac{44}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$x>\frac{44}{14}$$

Reduce the fraction \frac{44}{14} to lowest terms by extracting and canceling out 2.

$$x>\frac{22}{7}$$