Solve (x-2)-(2x-2)=(2x-1)-(x+2)

$$( x - 2 ) - ( 2 x - 2 ) = ( 2 x - 1 ) - ( x + 2 )$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

To find the opposite of 2x-2, find the opposite of each term.

$$x-2-2x-\left(-2\right)=2x-1-\left(x+2\right)$$

The opposite of -2 is 2.

$$x-2-2x+2=2x-1-\left(x+2\right)$$

Combine x and -2x to get -x.

$$-x-2+2=2x-1-\left(x+2\right)$$

Add -2 and 2 to get 0.

$$-x=2x-1-\left(x+2\right)$$

To find the opposite of x+2, find the opposite of each term.

$$-x=2x-1-x-2$$

Combine 2x and -x to get x.

$$-x=x-1-2$$

Subtract 2 from -1 to get -3.

$$-x=x-3$$

Subtract x from both sides.

$$-x-x=-3$$

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

$$-2x=-3$$

Divide both sides by -2.

$$x=\frac{-3}{-2}$$

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{2}$$