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

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

Solve for x

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

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

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

$$3x-2x+4-6=2x+x-1$$

Combine 3x and -2x to get x.

$$x+4-6=2x+x-1$$

Subtract 6 from 4 to get -2.

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

Combine 2x and x to get 3x.

$$x-2=3x-1$$

Subtract 3x from both sides.

$$x-2-3x=-1$$

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

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

Add 2 to both sides.

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

Add -1 and 2 to get 1.

$$-2x=1$$

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.

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