Solve 2/3u-2=-1/5u-5/3

$$\frac { 2 } { 3 } u - 2 = - \frac { 1 } { 5 } u - \frac { 5 } { 3 }$$

Solve for u

$$u=\frac{5}{13}\approx 0.384615385$$

Steps for Solving Linear Equation

Add \frac{1}{5}u to both sides.

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

Combine \frac{2}{3}u and \frac{1}{5}u to get \frac{13}{15}u.

$$\frac{13}{15}u-2=-\frac{5}{3}$$

Add 2 to both sides.

$$\frac{13}{15}u=-\frac{5}{3}+2$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{13}{15}u=-\frac{5}{3}+\frac{6}{3}$$

Since -\frac{5}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{13}{15}u=\frac{-5+6}{3}$$

Add -5 and 6 to get 1.

$$\frac{13}{15}u=\frac{1}{3}$$

Multiply both sides by \frac{15}{13}, the reciprocal of \frac{13}{15}.

$$u=\frac{1}{3}\times \frac{15}{13}$$

Multiply \frac{1}{3} times \frac{15}{13} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{1\times 15}{3\times 13}$$

Do the multiplications in the fraction \frac{1\times 15}{3\times 13}.

$$u=\frac{15}{39}$$

Reduce the fraction \frac{15}{39} to lowest terms by extracting and canceling out 3.

$$u=\frac{5}{13}$$