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

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

Solve for x

$$x<1$$

Solution Steps

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

$$x-3+6>2x+2$$

Add -3 and 6 to get 3.

$$x+3>2x+2$$

Subtract 2x from both sides.

$$x+3-2x>2$$

Combine x and -2x to get -x.

$$-x+3>2$$

Subtract 3 from both sides.

$$-x>2-3$$

Subtract 3 from 2 to get -1.

$$-x>-1$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

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

Divide -1 by -1 to get 1.

$$x<1$$