Solve 1/3/0.2=1/5-frac{a/7}{frac{1}{4}}

$$\frac { \frac { 1 } { 3 } } { 0.2 } = \frac { \frac { 1 } { 5 } - \frac { a } { 7 } } { \frac { 1 } { 4 } }$$

Solve for a

$$a = -\frac{91}{60} = -1\frac{31}{60} \approx -1.516666667$$

Steps for Solving Linear Equation

Express \frac{\frac{1}{3}}{0.2} as a single fraction.

$$\frac{1}{3\times 0.2}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

Multiply 3 and 0.2 to get 0.6.

$$\frac{1}{0.6}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

Expand \frac{1}{0.6} by multiplying both numerator and the denominator by 10.

$$\frac{10}{6}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 7 is 35. Multiply \frac{1}{5} times \frac{7}{7}. Multiply \frac{a}{7} times \frac{5}{5}.

$$\frac{5}{3}=\frac{\frac{7}{35}-\frac{5a}{35}}{\frac{1}{4}}$$

Since \frac{7}{35} and \frac{5a}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}=\frac{\frac{7-5a}{35}}{\frac{1}{4}}$$

Divide each term of 7-5a by 35 to get \frac{1}{5}-\frac{1}{7}a.

$$\frac{5}{3}=\frac{\frac{1}{5}-\frac{1}{7}a}{\frac{1}{4}}$$

Divide each term of \frac{1}{5}-\frac{1}{7}a by \frac{1}{4} to get \frac{\frac{1}{5}}{\frac{1}{4}}+\frac{-\frac{1}{7}a}{\frac{1}{4}}.

$$\frac{5}{3}=\frac{\frac{1}{5}}{\frac{1}{4}}+\frac{-\frac{1}{7}a}{\frac{1}{4}}$$

Divide \frac{1}{5} by \frac{1}{4} by multiplying \frac{1}{5} by the reciprocal of \frac{1}{4}.

$$\frac{5}{3}=\frac{1}{5}\times 4+\frac{-\frac{1}{7}a}{\frac{1}{4}}$$

Multiply \frac{1}{5} and 4 to get \frac{4}{5}.

$$\frac{5}{3}=\frac{4}{5}+\frac{-\frac{1}{7}a}{\frac{1}{4}}$$

Divide -\frac{1}{7}a by \frac{1}{4} to get -\frac{4}{7}a.

$$\frac{5}{3}=\frac{4}{5}-\frac{4}{7}a$$

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

$$\frac{4}{5}-\frac{4}{7}a=\frac{5}{3}$$

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

$$-\frac{4}{7}a=\frac{5}{3}-\frac{4}{5}$$

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

$$-\frac{4}{7}a=\frac{25}{15}-\frac{12}{15}$$

Since \frac{25}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4}{7}a=\frac{25-12}{15}$$

Subtract 12 from 25 to get 13.

$$-\frac{4}{7}a=\frac{13}{15}$$

Multiply both sides by -\frac{7}{4}, the reciprocal of -\frac{4}{7}.

$$a=\frac{13}{15}\left(-\frac{7}{4}\right)$$

Multiply \frac{13}{15} times -\frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{13\left(-7\right)}{15\times 4}$$

Do the multiplications in the fraction \frac{13\left(-7\right)}{15\times 4}.

$$a=\frac{-91}{60}$$

Fraction \frac{-91}{60} can be rewritten as -\frac{91}{60} by extracting the negative sign.

$$a=-\frac{91}{60}$$