Solve 3(x+5)(x-5)<(3x-20)x+5

$$3 ( x + 5 ) ( x - 5 ) < ( 3 x - 20 ) x + 5$$

Solve for x

$$x<4$$

Solution Steps

Use the distributive property to multiply 3 by x+5.

$$\left(3x+15\right)\left(x-5\right)<\left(3x-20\right)x+5$$

Use the distributive property to multiply 3x+15 by x-5 and combine like terms.

$$3x^{2}-75<\left(3x-20\right)x+5$$

Use the distributive property to multiply 3x-20 by x.

$$3x^{2}-75<3x^{2}-20x+5$$

Subtract 3x^{2} from both sides.

$$3x^{2}-75-3x^{2}<-20x+5$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-75<-20x+5$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$-20x+5>-75$$

Subtract 5 from both sides.

$$-20x>-75-5$$

Subtract 5 from -75 to get -80.

$$-20x>-80$$

Divide both sides by -20. Since -20 is negative, the inequality direction is changed.

$$x<\frac{-80}{-20}$$

Divide -80 by -20 to get 4.

$$x<4$$