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

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

Solve for x

$$x<\frac{1}{3}$$

Solution Steps

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

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

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

$$1-x<2-4x$$

Add 4x to both sides.

$$1-x+4x<2$$

Combine -x and 4x to get 3x.

$$1+3x<2$$

Subtract 1 from both sides.

$$3x<2-1$$

Subtract 1 from 2 to get 1.

$$3x<1$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x<\frac{1}{3}$$