Solve 10/19=-1/3-1/5f

$$\frac { 10 } { 19 } = - \frac { 1 } { 3 } - \frac { 1 } { 5 } f$$

Solve for f

$$f = -\frac{245}{57} = -4\frac{17}{57} \approx -4.298245614$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{3}-\frac{1}{5}f=\frac{10}{19}$$

Add \frac{1}{3} to both sides.

$$-\frac{1}{5}f=\frac{10}{19}+\frac{1}{3}$$

Least common multiple of 19 and 3 is 57. Convert \frac{10}{19} and \frac{1}{3} to fractions with denominator 57.

$$-\frac{1}{5}f=\frac{30}{57}+\frac{19}{57}$$

Since \frac{30}{57} and \frac{19}{57} have the same denominator, add them by adding their numerators.

$$-\frac{1}{5}f=\frac{30+19}{57}$$

Add 30 and 19 to get 49.

$$-\frac{1}{5}f=\frac{49}{57}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}.

$$f=\frac{49}{57}\left(-5\right)$$

Express \frac{49}{57}\left(-5\right) as a single fraction.

$$f=\frac{49\left(-5\right)}{57}$$

Multiply 49 and -5 to get -245.

$$f=\frac{-245}{57}$$

Fraction \frac{-245}{57} can be rewritten as -\frac{245}{57} by extracting the negative sign.

$$f=-\frac{245}{57}$$