Solve 2/5=1/3-2/3x

$$\frac{ 2 }{ 5 } = \frac{ 1 }{ 3 } - \frac{ 2 }{ 3 } x$$

Solve for x

$$x=-\frac{1}{10}=-0.1$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{3}-\frac{2}{3}x=\frac{2}{5}$$

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

$$-\frac{2}{3}x=\frac{2}{5}-\frac{1}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{1}{3} to fractions with denominator 15.

$$-\frac{2}{3}x=\frac{6}{15}-\frac{5}{15}$$

Since \frac{6}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x=\frac{6-5}{15}$$

Subtract 5 from 6 to get 1.

$$-\frac{2}{3}x=\frac{1}{15}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

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

Multiply \frac{1}{15} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\left(-3\right)}{15\times 2}$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{15\times 2}.

$$x=\frac{-3}{30}$$

Reduce the fraction \frac{-3}{30} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{10}$$