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

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

Solve for x

$$x>-4$$

Solution Steps

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

$$3\times 3x+7>5x-9$$

Multiply 3 and 3 to get 9.

$$9x+7>5x-9$$

Subtract 5x from both sides.

$$9x+7-5x>-9$$

Combine 9x and -5x to get 4x.

$$4x+7>-9$$

Subtract 7 from both sides.

$$4x>-9-7$$

Subtract 7 from -9 to get -16.

$$4x>-16$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x>\frac{-16}{4}$$

Divide -16 by 4 to get -4.

$$x>-4$$