Solve 7-x/2>5x/3-6

$$7 - \frac { x } { 2 } > \frac { 5 x } { 3 } - 6$$

Solve for x

$$x<6$$

Solution Steps

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

$$42-3x>2\times 5x-36$$

Multiply 2 and 5 to get 10.

$$42-3x>10x-36$$

Subtract 10x from both sides.

$$42-3x-10x>-36$$

Combine -3x and -10x to get -13x.

$$42-13x>-36$$

Subtract 42 from both sides.

$$-13x>-36-42$$

Subtract 42 from -36 to get -78.

$$-13x>-78$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x<\frac{-78}{-13}$$

Divide -78 by -13 to get 6.

$$x<6$$