Solve 1-2*left(x-1right)<2

$$1-2 \times \left( x-1 \right) < 2$$

Solve for x

$$x>\frac{1}{2}$$

Solution Steps

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

$$1-2x+2<2$$

Add 1 and 2 to get 3.

$$3-2x<2$$

Subtract 3 from both sides.

$$-2x<2-3$$

Subtract 3 from 2 to get -1.

$$-2x<-1$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x>\frac{-1}{-2}$$

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{1}{2}$$