Solve 7u-4/5=-6/5u-5/3

$$7 u - \frac { 4 } { 5 } = - \frac { 6 } { 5 } u - \frac { 5 } { 3 }$$

Solve for u

$$u=-\frac{13}{123}\approx -0.105691057$$

Steps for Solving Linear Equation

Add \frac{6}{5}u to both sides.

$$7u-\frac{4}{5}+\frac{6}{5}u=-\frac{5}{3}$$

Combine 7u and \frac{6}{5}u to get \frac{41}{5}u.

$$\frac{41}{5}u-\frac{4}{5}=-\frac{5}{3}$$

Add \frac{4}{5} to both sides.

$$\frac{41}{5}u=-\frac{5}{3}+\frac{4}{5}$$

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

$$\frac{41}{5}u=-\frac{25}{15}+\frac{12}{15}$$

Since -\frac{25}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{41}{5}u=\frac{-25+12}{15}$$

Add -25 and 12 to get -13.

$$\frac{41}{5}u=-\frac{13}{15}$$

Multiply both sides by \frac{5}{41}, the reciprocal of \frac{41}{5}.

$$u=-\frac{13}{15}\times \frac{5}{41}$$

Multiply -\frac{13}{15} times \frac{5}{41} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{-13\times 5}{15\times 41}$$

Do the multiplications in the fraction \frac{-13\times 5}{15\times 41}.

$$u=\frac{-65}{615}$$

Reduce the fraction \frac{-65}{615} to lowest terms by extracting and canceling out 5.

$$u=-\frac{13}{123}$$