Solve 2x-1/2-2x+5/3>6x-1/4-1

$$\frac{ 2x-1 }{ 2 } - \frac{ 2x+5 }{ 3 } > \frac{ 6x-1 }{ 4 } -1$$

Solve for x

$$x<-\frac{11}{14}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,3,4. Since 12 is positive, the inequality direction remains the same.

$$6\left(2x-1\right)-4\left(2x+5\right)>3\left(6x-1\right)-12$$

Use the distributive property to multiply 6 by 2x-1.

$$12x-6-4\left(2x+5\right)>3\left(6x-1\right)-12$$

Use the distributive property to multiply -4 by 2x+5.

$$12x-6-8x-20>3\left(6x-1\right)-12$$

Combine 12x and -8x to get 4x.

$$4x-6-20>3\left(6x-1\right)-12$$

Subtract 20 from -6 to get -26.

$$4x-26>3\left(6x-1\right)-12$$

Use the distributive property to multiply 3 by 6x-1.

$$4x-26>18x-3-12$$

Subtract 12 from -3 to get -15.

$$4x-26>18x-15$$

Subtract 18x from both sides.

$$4x-26-18x>-15$$

Combine 4x and -18x to get -14x.

$$-14x-26>-15$$

Add 26 to both sides.

$$-14x>-15+26$$

Add -15 and 26 to get 11.

$$-14x>11$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x<-\frac{11}{14}$$