Solve 5x-1/6+2>x+5/4

$$\frac{ 5x-1 }{ 6 } +2 > \frac{ x+5 }{ 4 }$$

Solve for x

$$x>-1$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 6,4. Since 12 is positive, the inequality direction remains the same.

$$2\left(5x-1\right)+24>3\left(x+5\right)$$

Use the distributive property to multiply 2 by 5x-1.

$$10x-2+24>3\left(x+5\right)$$

Add -2 and 24 to get 22.

$$10x+22>3\left(x+5\right)$$

Use the distributive property to multiply 3 by x+5.

$$10x+22>3x+15$$

Subtract 3x from both sides.

$$10x+22-3x>15$$

Combine 10x and -3x to get 7x.

$$7x+22>15$$

Subtract 22 from both sides.

$$7x>15-22$$

Subtract 22 from 15 to get -7.

$$7x>-7$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

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

Divide -7 by 7 to get -1.

$$x>-1$$