Solve (x-2)*(x+5)<(x-3)*(x-2)

$$(x-2) \times (x+5) < (x-3) \times (x-2)$$

Solve for x

$$x<2$$

Solution Steps

Use the distributive property to multiply x-2 by x+5 and combine like terms.

$$x^{2}+3x-10<\left(x-3\right)\left(x-2\right)$$

Use the distributive property to multiply x-3 by x-2 and combine like terms.

$$x^{2}+3x-10<x^{2}-5x+6$$

Subtract x^{2} from both sides.

$$x^{2}+3x-10-x^{2}<-5x+6$$

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

$$3x-10<-5x+6$$

Add 5x to both sides.

$$3x-10+5x<6$$

Combine 3x and 5x to get 8x.

$$8x-10<6$$

Add 10 to both sides.

$$8x<6+10$$

Add 6 and 10 to get 16.

$$8x<16$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x<\frac{16}{8}$$

Divide 16 by 8 to get 2.

$$x<2$$