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

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

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3,6.

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

Multiply 3 and 2 to get 6.

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

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

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

Use the distributive property to multiply -4 by 3x-2.

$$6x-6-12x+8=2x$$

Combine 6x and -12x to get -6x.

$$-6x-6+8=2x$$

Add -6 and 8 to get 2.

$$-6x+2=2x$$

Subtract 2x from both sides.

$$-6x+2-2x=0$$

Combine -6x and -2x to get -8x.

$$-8x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-8x=-2$$

Divide both sides by -8.

$$x=\frac{-2}{-8}$$

Reduce the fraction \frac{-2}{-8} to lowest terms by extracting and canceling out -2.

$$x=\frac{1}{4}$$