Solve 2x-1/4-x+6/2<x-4x-2/3

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

Solve for x

$$x<\frac{47}{4}$$

Solution Steps

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

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

Use the distributive property to multiply 3 by 2x-1.

$$6x-3-6\left(x+6\right)<12x-4\left(4x-2\right)$$

Use the distributive property to multiply -6 by x+6.

$$6x-3-6x-36<12x-4\left(4x-2\right)$$

Combine 6x and -6x to get 0.

$$-3-36<12x-4\left(4x-2\right)$$

Subtract 36 from -3 to get -39.

$$-39<12x-4\left(4x-2\right)$$

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

$$-39<12x-16x+8$$

Combine 12x and -16x to get -4x.

$$-39<-4x+8$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$-4x+8>-39$$

Subtract 8 from both sides.

$$-4x>-39-8$$

Subtract 8 from -39 to get -47.

$$-4x>-47$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{-47}{-4}$$

Fraction \frac{-47}{-4} can be simplified to \frac{47}{4} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{47}{4}$$