Solve 2/3x+4/5=x-1/3

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

Solve for x

$$x = \frac{17}{5} = 3\frac{2}{5} = 3.4$$

Steps for Solving Linear Equation

Subtract x from both sides.

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

Combine \frac{2}{3}x and -x to get -\frac{1}{3}x.

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

Subtract \frac{4}{5} from both sides.

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

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{4}{5} to fractions with denominator 15.

$$-\frac{1}{3}x=-\frac{5}{15}-\frac{12}{15}$$

Since -\frac{5}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x=\frac{-5-12}{15}$$

Subtract 12 from -5 to get -17.

$$-\frac{1}{3}x=-\frac{17}{15}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=-\frac{17}{15}\left(-3\right)$$

Express -\frac{17}{15}\left(-3\right) as a single fraction.

$$x=\frac{-17\left(-3\right)}{15}$$

Multiply -17 and -3 to get 51.

$$x=\frac{51}{15}$$

Reduce the fraction \frac{51}{15} to lowest terms by extracting and canceling out 3.

$$x=\frac{17}{5}$$