Solve (2x-1)(x+3)<(x+2)(2x-3)

$$( 2 x - 1 ) ( x + 3 ) < ( x + 2 ) ( 2 x - 3 )$$

Solve for x

$$x<-\frac{3}{4}$$

Solution Steps

Use the distributive property to multiply 2x-1 by x+3 and combine like terms.

$$2x^{2}+5x-3<\left(x+2\right)\left(2x-3\right)$$

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

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

Subtract 2x^{2} from both sides.

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

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

$$5x-3<x-6$$

Subtract x from both sides.

$$5x-3-x<-6$$

Combine 5x and -x to get 4x.

$$4x-3<-6$$

Add 3 to both sides.

$$4x<-6+3$$

Add -6 and 3 to get -3.

$$4x<-3$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x<-\frac{3}{4}$$