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

$$(x-1) \times (2x-2) > (2x-1) \times (x+2)$$

Solve for x

$$x<\frac{4}{7}$$

Solution Steps

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

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

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

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

Subtract 2x^{2} from both sides.

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

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

$$-4x+2>3x-2$$

Subtract 3x from both sides.

$$-4x+2-3x>-2$$

Combine -4x and -3x to get -7x.

$$-7x+2>-2$$

Subtract 2 from both sides.

$$-7x>-2-2$$

Subtract 2 from -2 to get -4.

$$-7x>-4$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x<\frac{-4}{-7}$$

Fraction \frac{-4}{-7} can be simplified to \frac{4}{7} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{4}{7}$$