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

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

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

$$30\left(\frac{x}{2}+\frac{1}{6}\right)-2=6x-12\left(1-\frac{x}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 6 is 6. Multiply \frac{x}{2} times \frac{3}{3}.

$$30\left(\frac{3x}{6}+\frac{1}{6}\right)-2=6x-12\left(1-\frac{x}{3}\right)$$

Since \frac{3x}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$30\times \frac{3x+1}{6}-2=6x-12\left(1-\frac{x}{3}\right)$$

Cancel out 6, the greatest common factor in 30 and 6.

$$5\left(3x+1\right)-2=6x-12\left(1-\frac{x}{3}\right)$$

Use the distributive property to multiply 5 by 3x+1.

$$15x+5-2=6x-12\left(1-\frac{x}{3}\right)$$

Subtract 2 from 5 to get 3.

$$15x+3=6x-12\left(1-\frac{x}{3}\right)$$

Add 12\left(1-\frac{x}{3}\right) to both sides.

$$15x+3+12\left(1-\frac{x}{3}\right)=6x$$

Use the distributive property to multiply 12 by 1-\frac{x}{3}.

$$15x+3+12+12\left(-\frac{x}{3}\right)=6x$$

Cancel out 3, the greatest common factor in 12 and 3.

$$15x+3+12-4x=6x$$

Add 3 and 12 to get 15.

$$15x+15-4x=6x$$

Combine 15x and -4x to get 11x.

$$11x+15=6x$$

Subtract 6x from both sides.

$$11x+15-6x=0$$

Combine 11x and -6x to get 5x.

$$5x+15=0$$

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$5x=-15$$

Divide both sides by 5.

$$x=\frac{-15}{5}$$

Divide -15 by 5 to get -3.

$$x=-3$$