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

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

Solve for x

$$x>\frac{23}{63}$$

Solution Steps

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

$$24-3\left(1-x\right)<72x-2\left(3x+1\right)$$

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

$$24-3+3x<72x-2\left(3x+1\right)$$

Subtract 3 from 24 to get 21.

$$21+3x<72x-2\left(3x+1\right)$$

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

$$21+3x<72x-6x-2$$

Combine 72x and -6x to get 66x.

$$21+3x<66x-2$$

Subtract 66x from both sides.

$$21+3x-66x<-2$$

Combine 3x and -66x to get -63x.

$$21-63x<-2$$

Subtract 21 from both sides.

$$-63x<-2-21$$

Subtract 21 from -2 to get -23.

$$-63x<-23$$

Divide both sides by -63. Since -63 is negative, the inequality direction is changed.

$$x>\frac{-23}{-63}$$

Fraction \frac{-23}{-63} can be simplified to \frac{23}{63} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{23}{63}$$