Solve x-1/2<x

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

Solve for x

$$x>-1$$

Solution Steps

Divide each term of x-1 by 2 to get \frac{1}{2}x-\frac{1}{2}.

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

Subtract x from both sides.

$$\frac{1}{2}x-\frac{1}{2}-x<0$$

Combine \frac{1}{2}x and -x to get -\frac{1}{2}x.

$$-\frac{1}{2}x-\frac{1}{2}<0$$

Add \frac{1}{2} to both sides. Anything plus zero gives itself.

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

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$x>\frac{1}{2}\left(-2\right)$$

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

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

Divide -2 by 2 to get -1.

$$x>-1$$