Solve x-6(1-x)+3(4-2x)/5=3(x+1/6)-2

$$x - \frac { 6 ( 1 - x ) + 3 ( 4 - 2 x ) } { 5 } = 3 ( x + \frac { 1 } { 6 } ) - 2$$

Solve for x

$$x = \frac{21}{4} = 5\frac{1}{4} = 5.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6.

$$30x-6\left(6\left(1-x\right)+3\left(4-2x\right)\right)=90\left(x+\frac{1}{6}\right)-60$$

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

$$30x-6\left(6-6x+3\left(4-2x\right)\right)=90\left(x+\frac{1}{6}\right)-60$$

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

$$30x-6\left(6-6x+12-6x\right)=90\left(x+\frac{1}{6}\right)-60$$

Add 6 and 12 to get 18.

$$30x-6\left(18-6x-6x\right)=90\left(x+\frac{1}{6}\right)-60$$

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

$$30x-6\left(18-12x\right)=90\left(x+\frac{1}{6}\right)-60$$

Use the distributive property to multiply -6 by 18-12x.

$$30x-108+72x=90\left(x+\frac{1}{6}\right)-60$$

Combine 30x and 72x to get 102x.

$$102x-108=90\left(x+\frac{1}{6}\right)-60$$

Use the distributive property to multiply 90 by x+\frac{1}{6}.

$$102x-108=90x+90\times \frac{1}{6}-60$$

Multiply 90 and \frac{1}{6} to get \frac{90}{6}.

$$102x-108=90x+\frac{90}{6}-60$$

Divide 90 by 6 to get 15.

$$102x-108=90x+15-60$$

Subtract 60 from 15 to get -45.

$$102x-108=90x-45$$

Subtract 90x from both sides.

$$102x-108-90x=-45$$

Combine 102x and -90x to get 12x.

$$12x-108=-45$$

Add 108 to both sides.

$$12x=-45+108$$

Add -45 and 108 to get 63.

$$12x=63$$

Divide both sides by 12.

$$x=\frac{63}{12}$$

Reduce the fraction \frac{63}{12} to lowest terms by extracting and canceling out 3.

$$x=\frac{21}{4}$$