Solve x+2geq3(x-1)

$$x + 2 \geq 3 ( x - 1 )$$

Solve for x

$$x\leq \frac{5}{2}$$

Solution Steps

Use the distributive property to multiply 3 by x-1.

$$x+2\geq 3x-3$$

Subtract 3x from both sides.

$$x+2-3x\geq -3$$

Combine x and -3x to get -2x.

$$-2x+2\geq -3$$

Subtract 2 from both sides.

$$-2x\geq -3-2$$

Subtract 2 from -3 to get -5.

$$-2x\geq -5$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\leq \frac{-5}{-2}$$

Fraction \frac{-5}{-2} can be simplified to \frac{5}{2} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{5}{2}$$