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

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

Solve for x

$$x=\frac{2}{5}=0.4$$

Steps for Solving Linear Equation

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

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

The opposite of -\frac{1}{3} is \frac{1}{3}.

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

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

$$x+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}$$

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

$$x+\frac{1}{3}=\frac{6+5}{15}$$

Add 6 and 5 to get 11.

$$x+\frac{1}{3}=\frac{11}{15}$$

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

$$x=\frac{11}{15}-\frac{1}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{11}{15} and \frac{1}{3} to fractions with denominator 15.

$$x=\frac{11}{15}-\frac{5}{15}$$

Since \frac{11}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{11-5}{15}$$

Subtract 5 from 11 to get 6.

$$x=\frac{6}{15}$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$x=\frac{2}{5}$$