Solve 4/3w-2/3=3w-7/5

$$\frac { 4 } { 3 } w - \frac { 2 } { 3 } = 3 w - \frac { 7 } { 5 }$$

Solve for w

$$w=\frac{11}{25}=0.44$$

Steps for Solving Linear Equation

Subtract 3w from both sides.

$$\frac{4}{3}w-\frac{2}{3}-3w=-\frac{7}{5}$$

Combine \frac{4}{3}w and -3w to get -\frac{5}{3}w.

$$-\frac{5}{3}w-\frac{2}{3}=-\frac{7}{5}$$

Add \frac{2}{3} to both sides.

$$-\frac{5}{3}w=-\frac{7}{5}+\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{7}{5} and \frac{2}{3} to fractions with denominator 15.

$$-\frac{5}{3}w=-\frac{21}{15}+\frac{10}{15}$$

Since -\frac{21}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$-\frac{5}{3}w=\frac{-21+10}{15}$$

Add -21 and 10 to get -11.

$$-\frac{5}{3}w=-\frac{11}{15}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}.

$$w=-\frac{11}{15}\left(-\frac{3}{5}\right)$$

Multiply -\frac{11}{15} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{-11\left(-3\right)}{15\times 5}$$

Do the multiplications in the fraction \frac{-11\left(-3\right)}{15\times 5}.

$$w=\frac{33}{75}$$

Reduce the fraction \frac{33}{75} to lowest terms by extracting and canceling out 3.

$$w=\frac{11}{25}$$