Solve x/3+x/2>5-x/6

$$\frac { x } { 3 } + \frac { x } { 2 } > 5 - \frac { x } { 6 }$$

Solve for x

$$x>5$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2,6. Since 6 is positive, the inequality direction remains the same.

$$2x+3x>30-x$$

Combine 2x and 3x to get 5x.

$$5x>30-x$$

Add x to both sides.

$$5x+x>30$$

Combine 5x and x to get 6x.

$$6x>30$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x>\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$x>5$$