Solve 1/4(2x-1)-x<x/6-1/3

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

Solve for x

$$x>\frac{1}{8}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6,3. Since 12 is positive, the inequality direction remains the same.

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

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

$$6x-3-12x<2x-4$$

Combine 6x and -12x to get -6x.

$$-6x-3<2x-4$$

Subtract 2x from both sides.

$$-6x-3-2x<-4$$

Combine -6x and -2x to get -8x.

$$-8x-3<-4$$

Add 3 to both sides.

$$-8x<-4+3$$

Add -4 and 3 to get -1.

$$-8x<-1$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x>\frac{-1}{-8}$$

Fraction \frac{-1}{-8} can be simplified to \frac{1}{8} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{1}{8}$$