Solve 2x-5/6>3x-x+2/4

$$\frac{ 2x-5 }{ 6 } > 3x- \frac{ x+2 }{ 4 }$$

Solve for x

$$x<-\frac{4}{29}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 6,4. Since 12 is positive, the inequality direction remains the same.

$$2\left(2x-5\right)>36x-3\left(x+2\right)$$

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

$$4x-10>36x-3\left(x+2\right)$$

Use the distributive property to multiply -3 by x+2.

$$4x-10>36x-3x-6$$

Combine 36x and -3x to get 33x.

$$4x-10>33x-6$$

Subtract 33x from both sides.

$$4x-10-33x>-6$$

Combine 4x and -33x to get -29x.

$$-29x-10>-6$$

Add 10 to both sides.

$$-29x>-6+10$$

Add -6 and 10 to get 4.

$$-29x>4$$

Divide both sides by -29. Since -29 is negative, the inequality direction is changed.

$$x<-\frac{4}{29}$$