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

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

Solve for x

$$x>2$$

Solution Steps

Multiply both sides of the equation by 28, the least common multiple of 4,7. Since 28 is positive, the inequality direction remains the same.

$$7\left(5x-6\right)>4\left(x+5\right)$$

Use the distributive property to multiply 7 by 5x-6.

$$35x-42>4\left(x+5\right)$$

Use the distributive property to multiply 4 by x+5.

$$35x-42>4x+20$$

Subtract 4x from both sides.

$$35x-42-4x>20$$

Combine 35x and -4x to get 31x.

$$31x-42>20$$

Add 42 to both sides.

$$31x>20+42$$

Add 20 and 42 to get 62.

$$31x>62$$

Divide both sides by 31. Since 31 is positive, the inequality direction remains the same.

$$x>\frac{62}{31}$$

Divide 62 by 31 to get 2.

$$x>2$$