Solve (x+5)(x+3)geq(x+9)(x+1)

$$(x+5)(x+3) \geq (x+9)(x+1)$$

Solve for x

$$x\leq 3$$

Solution Steps

Use the distributive property to multiply x+5 by x+3 and combine like terms.

$$x^{2}+8x+15\geq \left(x+9\right)\left(x+1\right)$$

Use the distributive property to multiply x+9 by x+1 and combine like terms.

$$x^{2}+8x+15\geq x^{2}+10x+9$$

Subtract x^{2} from both sides.

$$x^{2}+8x+15-x^{2}\geq 10x+9$$

Combine x^{2} and -x^{2} to get 0.

$$8x+15\geq 10x+9$$

Subtract 10x from both sides.

$$8x+15-10x\geq 9$$

Combine 8x and -10x to get -2x.

$$-2x+15\geq 9$$

Subtract 15 from both sides.

$$-2x\geq 9-15$$

Subtract 15 from 9 to get -6.

$$-2x\geq -6$$

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

$$x\leq \frac{-6}{-2}$$

Divide -6 by -2 to get 3.

$$x\leq 3$$