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

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

Solve for x

$$x<4$$

Solution Steps

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

$$x^{2}-6x+8>\left(x-4\right)\left(x+1\right)$$

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

$$x^{2}-6x+8>x^{2}-3x-4$$

Subtract x^{2} from both sides.

$$x^{2}-6x+8-x^{2}>-3x-4$$

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

$$-6x+8>-3x-4$$

Add 3x to both sides.

$$-6x+8+3x>-4$$

Combine -6x and 3x to get -3x.

$$-3x+8>-4$$

Subtract 8 from both sides.

$$-3x>-4-8$$

Subtract 8 from -4 to get -12.

$$-3x>-12$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<\frac{-12}{-3}$$

Divide -12 by -3 to get 4.

$$x<4$$