Solve x+1/2geqx-2

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

Solve for x

$$x\leq 5$$

Solution Steps

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

$$x+1\geq 2x-4$$

Subtract 2x from both sides.

$$x+1-2x\geq -4$$

Combine x and -2x to get -x.

$$-x+1\geq -4$$

Subtract 1 from both sides.

$$-x\geq -4-1$$

Subtract 1 from -4 to get -5.

$$-x\geq -5$$

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

$$x\leq \frac{-5}{-1}$$

Fraction \frac{-5}{-1} can be simplified to 5 by removing the negative sign from both the numerator and the denominator.

$$x\leq 5$$