Solve 3x-4/2>5x-2/3

$$\frac { 3 x - 4 } { 2 } > \frac { 5 x - 2 } { 3 }$$

Solve for x

$$x<-8$$

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.

$$3\left(3x-4\right)>2\left(5x-2\right)$$

Use the distributive property to multiply 3 by 3x-4.

$$9x-12>2\left(5x-2\right)$$

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

$$9x-12>10x-4$$

Subtract 10x from both sides.

$$9x-12-10x>-4$$

Combine 9x and -10x to get -x.

$$-x-12>-4$$

Add 12 to both sides.

$$-x>-4+12$$

Add -4 and 12 to get 8.

$$-x>8$$

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

$$x<-8$$