Solve -(x-2)+3(x-1)+2=0

$$- ( x - 2 ) + 3 ( x - 1 ) + 2 = 0$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

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

$$-x-\left(-2\right)+3\left(x-1\right)+2=0$$

The opposite of -2 is 2.

$$-x+2+3\left(x-1\right)+2=0$$

Use the distributive property to multiply 3 by x-1.

$$-x+2+3x-3+2=0$$

Combine -x and 3x to get 2x.

$$2x+2-3+2=0$$

Subtract 3 from 2 to get -1.

$$2x-1+2=0$$

Add -1 and 2 to get 1.

$$2x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$2x=-1$$

Divide both sides by 2.

$$x=\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x=-\frac{1}{2}$$