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

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

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-\frac{2}{3}.

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

Express 2\left(-\frac{2}{3}\right) as a single fraction.

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

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

$$x+\frac{1}{3}=-4x-\frac{4}{3}$$

Add 4x to both sides.

$$x+\frac{1}{3}+4x=-\frac{4}{3}$$

Combine x and 4x to get 5x.

$$5x+\frac{1}{3}=-\frac{4}{3}$$

Subtract \frac{1}{3} from both sides.

$$5x=-\frac{4}{3}-\frac{1}{3}$$

Since -\frac{4}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$5x=\frac{-4-1}{3}$$

Subtract 1 from -4 to get -5.

$$5x=-\frac{5}{3}$$

Divide both sides by 5.

$$x=\frac{-\frac{5}{3}}{5}$$

Express \frac{-\frac{5}{3}}{5} as a single fraction.

$$x=\frac{-5}{3\times 5}$$

Multiply 3 and 5 to get 15.

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

Reduce the fraction \frac{-5}{15} to lowest terms by extracting and canceling out 5.

$$x=-\frac{1}{3}$$