Solve (x-1)-1/2(x+2)+1/3(x-3)=-4

$$( x - 1 ) - \frac { 1 } { 2 } ( x + 2 ) + \frac { 1 } { 3 } ( x - 3 ) = - 4$$

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{2} by x+2.

$$x-1-\frac{1}{2}x-\frac{1}{2}\times 2+\frac{1}{3}\left(x-3\right)=-4$$

Cancel out 2 and 2.

$$x-1-\frac{1}{2}x-1+\frac{1}{3}\left(x-3\right)=-4$$

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

$$\frac{1}{2}x-1-1+\frac{1}{3}\left(x-3\right)=-4$$

Subtract 1 from -1 to get -2.

$$\frac{1}{2}x-2+\frac{1}{3}\left(x-3\right)=-4$$

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

$$\frac{1}{2}x-2+\frac{1}{3}x+\frac{1}{3}\left(-3\right)=-4$$

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

$$\frac{1}{2}x-2+\frac{1}{3}x+\frac{-3}{3}=-4$$

Divide -3 by 3 to get -1.

$$\frac{1}{2}x-2+\frac{1}{3}x-1=-4$$

Combine \frac{1}{2}x and \frac{1}{3}x to get \frac{5}{6}x.

$$\frac{5}{6}x-2-1=-4$$

Subtract 1 from -2 to get -3.

$$\frac{5}{6}x-3=-4$$

Add 3 to both sides.

$$\frac{5}{6}x=-4+3$$

Add -4 and 3 to get -1.

$$\frac{5}{6}x=-1$$

Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.

$$x=-\frac{6}{5}$$