Solve x-1/2-3x-2/6=1/3(x-4)-2x-1/4

$$\frac { x - 1 } { 2 } - \frac { 3 x - 2 } { 6 } = \frac { 1 } { 3 } ( x - 4 ) - \frac { 2 x - 1 } { 4 }$$

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 12, the least common multiple of 2,6,3,4.

$$6\left(x-1\right)-2\left(3x-2\right)=4\left(x-4\right)-3\left(2x-1\right)$$

Use the distributive property to multiply 6 by x-1.

$$6x-6-2\left(3x-2\right)=4\left(x-4\right)-3\left(2x-1\right)$$

Use the distributive property to multiply -2 by 3x-2.

$$6x-6-6x+4=4\left(x-4\right)-3\left(2x-1\right)$$

Combine 6x and -6x to get 0.

$$-6+4=4\left(x-4\right)-3\left(2x-1\right)$$

Add -6 and 4 to get -2.

$$-2=4\left(x-4\right)-3\left(2x-1\right)$$

Use the distributive property to multiply 4 by x-4.

$$-2=4x-16-3\left(2x-1\right)$$

Use the distributive property to multiply -3 by 2x-1.

$$-2=4x-16-6x+3$$

Combine 4x and -6x to get -2x.

$$-2=-2x-16+3$$

Add -16 and 3 to get -13.

$$-2=-2x-13$$

Swap sides so that all variable terms are on the left hand side.

$$-2x-13=-2$$

Add 13 to both sides.

$$-2x=-2+13$$

Add -2 and 13 to get 11.

$$-2x=11$$

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.

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