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

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

Solve for x

$$x=-\frac{1}{15}\approx -0.066666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by \frac{1}{5}-x.

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

Multiply 4 and \frac{1}{5} to get \frac{4}{5}.

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

Add 4x to both sides.

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

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

$$-2x+\frac{2}{3}=\frac{4}{5}$$

Subtract \frac{2}{3} from both sides.

$$-2x=\frac{4}{5}-\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{2}{3} to fractions with denominator 15.

$$-2x=\frac{12}{15}-\frac{10}{15}$$

Since \frac{12}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$-2x=\frac{12-10}{15}$$

Subtract 10 from 12 to get 2.

$$-2x=\frac{2}{15}$$

Divide both sides by -2.

$$x=\frac{\frac{2}{15}}{-2}$$

Express \frac{\frac{2}{15}}{-2} as a single fraction.

$$x=\frac{2}{15\left(-2\right)}$$

Multiply 15 and -2 to get -30.

$$x=\frac{2}{-30}$$

Reduce the fraction \frac{2}{-30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{15}$$