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

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

Solve for x

$$x>\frac{11}{8}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

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

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

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

Add 2 and 3 to get 5.

$$5-2x<3\left(2x-2\right)$$

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

$$5-2x<6x-6$$

Subtract 6x from both sides.

$$5-2x-6x<-6$$

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

$$5-8x<-6$$

Subtract 5 from both sides.

$$-8x<-6-5$$

Subtract 5 from -6 to get -11.

$$-8x<-11$$

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

$$x>\frac{-11}{-8}$$

Fraction \frac{-11}{-8} can be simplified to \frac{11}{8} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{11}{8}$$