Solve 3[x-2(x-2)]>x-3(x-3)

$$3 [ x - 2 ( x - 2 ) ] > x - 3 ( x - 3 )$$

Solve for x

$$x<3$$

Solution Steps

Use the distributive property to multiply -2 by x-2.

$$3\left(x-2x+4\right)>x-3\left(x-3\right)$$

Combine x and -2x to get -x.

$$3\left(-x+4\right)>x-3\left(x-3\right)$$

Use the distributive property to multiply 3 by -x+4.

$$-3x+12>x-3\left(x-3\right)$$

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

$$-3x+12>x-3x+9$$

Combine x and -3x to get -2x.

$$-3x+12>-2x+9$$

Add 2x to both sides.

$$-3x+12+2x>9$$

Combine -3x and 2x to get -x.

$$-x+12>9$$

Subtract 12 from both sides.

$$-x>9-12$$

Subtract 12 from 9 to get -3.

$$-x>-3$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<\frac{-3}{-1}$$

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$x<3$$