Solve 1/5(2f-3)+1/6(f-4)+2/15=0

$$\frac { 1 } { 5 } ( 2 f - 3 ) + \frac { 1 } { 6 } ( f - 4 ) + \frac { 2 } { 15 } = 0$$

Solve for f

$$f=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by 2f-3.

$$\frac{1}{5}\times 2f+\frac{1}{5}\left(-3\right)+\frac{1}{6}\left(f-4\right)+\frac{2}{15}=0$$

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

$$\frac{2}{5}f+\frac{1}{5}\left(-3\right)+\frac{1}{6}\left(f-4\right)+\frac{2}{15}=0$$

Multiply \frac{1}{5} and -3 to get \frac{-3}{5}.

$$\frac{2}{5}f+\frac{-3}{5}+\frac{1}{6}\left(f-4\right)+\frac{2}{15}=0$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{2}{5}f-\frac{3}{5}+\frac{1}{6}\left(f-4\right)+\frac{2}{15}=0$$

Use the distributive property to multiply \frac{1}{6} by f-4.

$$\frac{2}{5}f-\frac{3}{5}+\frac{1}{6}f+\frac{1}{6}\left(-4\right)+\frac{2}{15}=0$$

Multiply \frac{1}{6} and -4 to get \frac{-4}{6}.

$$\frac{2}{5}f-\frac{3}{5}+\frac{1}{6}f+\frac{-4}{6}+\frac{2}{15}=0$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}f-\frac{3}{5}+\frac{1}{6}f-\frac{2}{3}+\frac{2}{15}=0$$

Combine \frac{2}{5}f and \frac{1}{6}f to get \frac{17}{30}f.

$$\frac{17}{30}f-\frac{3}{5}-\frac{2}{3}+\frac{2}{15}=0$$

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

$$\frac{17}{30}f-\frac{9}{15}-\frac{10}{15}+\frac{2}{15}=0$$

Since -\frac{9}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{30}f+\frac{-9-10}{15}+\frac{2}{15}=0$$

Subtract 10 from -9 to get -19.

$$\frac{17}{30}f-\frac{19}{15}+\frac{2}{15}=0$$

Since -\frac{19}{15} and \frac{2}{15} have the same denominator, add them by adding their numerators.

$$\frac{17}{30}f+\frac{-19+2}{15}=0$$

Add -19 and 2 to get -17.

$$\frac{17}{30}f-\frac{17}{15}=0$$

Add \frac{17}{15} to both sides. Anything plus zero gives itself.

$$\frac{17}{30}f=\frac{17}{15}$$

Multiply both sides by \frac{30}{17}, the reciprocal of \frac{17}{30}.

$$f=\frac{17}{15}\times \frac{30}{17}$$

Multiply \frac{17}{15} times \frac{30}{17} by multiplying numerator times numerator and denominator times denominator.

$$f=\frac{17\times 30}{15\times 17}$$

Cancel out 17 in both numerator and denominator.

$$f=\frac{30}{15}$$

Divide 30 by 15 to get 2.

$$f=2$$