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

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

Solve for x

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

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

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

To find the opposite of 1-2x, find the opposite of each term.

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

The opposite of -2x is 2x.

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

Subtract 1 from 1 to get 0.

$$2x+2x<2$$

Combine 2x and 2x to get 4x.

$$4x<2$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x<\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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