Solve -(x-3)+1/3(x-6)=x-2

$$-(x-3)+ \frac{ 1 }{ 3 } (x-6)=x-2$$

Solve for x

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

Steps for Solving Linear Equation

To find the opposite of x-3, find the opposite of each term.

$$-x-\left(-3\right)+\frac{1}{3}\left(x-6\right)=x-2$$

The opposite of -3 is 3.

$$-x+3+\frac{1}{3}\left(x-6\right)=x-2$$

Use the distributive property to multiply \frac{1}{3} by x-6.

$$-x+3+\frac{1}{3}x+\frac{1}{3}\left(-6\right)=x-2$$

Multiply \frac{1}{3} and -6 to get \frac{-6}{3}.

$$-x+3+\frac{1}{3}x+\frac{-6}{3}=x-2$$

Divide -6 by 3 to get -2.

$$-x+3+\frac{1}{3}x-2=x-2$$

Combine -x and \frac{1}{3}x to get -\frac{2}{3}x.

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

Subtract 2 from 3 to get 1.

$$-\frac{2}{3}x+1=x-2$$

Subtract x from both sides.

$$-\frac{2}{3}x+1-x=-2$$

Combine -\frac{2}{3}x and -x to get -\frac{5}{3}x.

$$-\frac{5}{3}x+1=-2$$

Subtract 1 from both sides.

$$-\frac{5}{3}x=-2-1$$

Subtract 1 from -2 to get -3.

$$-\frac{5}{3}x=-3$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}.

$$x=-3\left(-\frac{3}{5}\right)$$

Express -3\left(-\frac{3}{5}\right) as a single fraction.

$$x=\frac{-3\left(-3\right)}{5}$$

Multiply -3 and -3 to get 9.

$$x=\frac{9}{5}$$