Solve 2x/7-3/2>5x-6/14

$$\frac { 2 x } { 7 } - \frac { 3 } { 2 } > \frac { 5 x - 6 } { 14 }$$

Solve for x

$$x<-15$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 7,2,14. Since 14 is positive, the inequality direction remains the same.

$$2\times 2x-21>5x-6$$

Multiply 2 and 2 to get 4.

$$4x-21>5x-6$$

Subtract 5x from both sides.

$$4x-21-5x>-6$$

Combine 4x and -5x to get -x.

$$-x-21>-6$$

Add 21 to both sides.

$$-x>-6+21$$

Add -6 and 21 to get 15.

$$-x>15$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<-15$$