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

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

Solve for w

$$w=-\frac{24}{47}\approx -0.510638298$$

Steps for Solving Linear Equation

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

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

Combine -\frac{7}{3}w and -\frac{4}{5}w to get -\frac{47}{15}w.

$$-\frac{47}{15}w-2=-\frac{2}{5}$$

Add 2 to both sides.

$$-\frac{47}{15}w=-\frac{2}{5}+2$$

Convert 2 to fraction \frac{10}{5}.

$$-\frac{47}{15}w=-\frac{2}{5}+\frac{10}{5}$$

Since -\frac{2}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$-\frac{47}{15}w=\frac{-2+10}{5}$$

Add -2 and 10 to get 8.

$$-\frac{47}{15}w=\frac{8}{5}$$

Multiply both sides by -\frac{15}{47}, the reciprocal of -\frac{47}{15}.

$$w=\frac{8}{5}\left(-\frac{15}{47}\right)$$

Multiply \frac{8}{5} times -\frac{15}{47} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{8\left(-15\right)}{5\times 47}$$

Do the multiplications in the fraction \frac{8\left(-15\right)}{5\times 47}.

$$w=\frac{-120}{235}$$

Reduce the fraction \frac{-120}{235} to lowest terms by extracting and canceling out 5.

$$w=-\frac{24}{47}$$