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

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

Solve for x

$$x = -\frac{11}{2} = -5\frac{1}{2} = -5.5$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply -2 by 2x+1.

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

Combine 3x and -4x to get -x.

$$-x-3-2-x=6$$

Subtract 2 from -3 to get -5.

$$-x-5-x=6$$

Add 5 to both sides.

$$-x-x=6+5$$

Add 6 and 5 to get 11.

$$-x-x=11$$

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

$$-2x=11$$

Divide both sides by -2.

$$x=\frac{11}{-2}$$

Fraction \frac{11}{-2} can be rewritten as -\frac{11}{2} by extracting the negative sign.

$$x=-\frac{11}{2}$$