Solve -4/5t+2/5=2/3

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

Solve for t

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

Steps for Solving Linear Equation

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

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

Subtract \frac{2}{5} from both sides.

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

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

$$-\frac{4}{5}t=\frac{10}{15}-\frac{6}{15}$$

Since \frac{10}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4}{5}t=\frac{10-6}{15}$$

Subtract 6 from 10 to get 4.

$$-\frac{4}{5}t=\frac{4}{15}$$

Multiply both sides by -\frac{5}{4}, the reciprocal of -\frac{4}{5}.

$$t=\frac{4}{15}\left(-\frac{5}{4}\right)$$

Multiply \frac{4}{15} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{4\left(-5\right)}{15\times 4}$$

Cancel out 4 in both numerator and denominator.

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

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

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