Solve 2x+9geq3(x+2)

$$2x+9 \geq 3(x+2)$$

Solve for x

$$x\leq 3$$

Solution Steps

Use the distributive property to multiply 3 by x+2.

$$2x+9\geq 3x+6$$

Subtract 3x from both sides.

$$2x+9-3x\geq 6$$

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

$$-x+9\geq 6$$

Subtract 9 from both sides.

$$-x\geq 6-9$$

Subtract 9 from 6 to get -3.

$$-x\geq -3$$

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

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

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

$$x\leq 3$$