Solve x-5/2+1>x-3

$$\frac { x - 5 } { 2 } + 1 > x - 3$$

Solve for x

$$x<3$$

Solution Steps

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

$$x-5+2>2x-6$$

Add -5 and 2 to get -3.

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

Subtract 2x from both sides.

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

Combine x and -2x to get -x.

$$-x-3>-6$$

Add 3 to both sides.

$$-x>-6+3$$

Add -6 and 3 to get -3.

$$-x>-3$$

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

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

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$x<3$$