Solve (4x+1)(2x-2)>8x(x+5)

$$(4x+1)(2x-2) > 8x(x+5)$$

Solve for x

$$x<-\frac{1}{23}$$

Solution Steps

Use the distributive property to multiply 4x+1 by 2x-2 and combine like terms.

$$8x^{2}-6x-2>8x\left(x+5\right)$$

Use the distributive property to multiply 8x by x+5.

$$8x^{2}-6x-2>8x^{2}+40x$$

Subtract 8x^{2} from both sides.

$$8x^{2}-6x-2-8x^{2}>40x$$

Combine 8x^{2} and -8x^{2} to get 0.

$$-6x-2>40x$$

Subtract 40x from both sides.

$$-6x-2-40x>0$$

Combine -6x and -40x to get -46x.

$$-46x-2>0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-46x>2$$

Divide both sides by -46. Since -46 is negative, the inequality direction is changed.

$$x<\frac{2}{-46}$$

Reduce the fraction \frac{2}{-46} to lowest terms by extracting and canceling out 2.

$$x<-\frac{1}{23}$$