Solve (7/12-1/4)div5/12-(Delta-2/3)=frac{1}{5}

$$( \frac { 7 } { 12 } - \frac { 1 } { 4 } ) \div \frac { 5 } { 12 } - ( \Delta - \frac { 2 } { 3 } ) = \frac { 1 } { 5 }$$

Solve for Δ

$$\Delta =\frac{19}{15}\approx 1.266666667$$

Steps for Solving Linear Equation

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{7}{12}-\frac{3}{12}}{\frac{5}{12}}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

Since \frac{7}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-3}{12}}{\frac{5}{12}}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

Subtract 3 from 7 to get 4.

$$\frac{\frac{4}{12}}{\frac{5}{12}}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{1}{3}}{\frac{5}{12}}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

Divide \frac{1}{3} by \frac{5}{12} by multiplying \frac{1}{3} by the reciprocal of \frac{5}{12}.

$$\frac{1}{3}\times \frac{12}{5}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

Multiply \frac{1}{3} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 12}{3\times 5}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

Do the multiplications in the fraction \frac{1\times 12}{3\times 5}.

$$\frac{12}{15}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}-\left(\Delta -\frac{2}{3}\right)=\frac{1}{5}$$

To find the opposite of \Delta -\frac{2}{3}, find the opposite of each term.

$$\frac{4}{5}-\Delta -\left(-\frac{2}{3}\right)=\frac{1}{5}$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\frac{4}{5}-\Delta +\frac{2}{3}=\frac{1}{5}$$

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{12}{15}-\Delta +\frac{10}{15}=\frac{1}{5}$$

Since \frac{12}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{12+10}{15}-\Delta =\frac{1}{5}$$

Add 12 and 10 to get 22.

$$\frac{22}{15}-\Delta =\frac{1}{5}$$

Subtract \frac{22}{15} from both sides.

$$-\Delta =\frac{1}{5}-\frac{22}{15}$$

Least common multiple of 5 and 15 is 15. Convert \frac{1}{5} and \frac{22}{15} to fractions with denominator 15.

$$-\Delta =\frac{3}{15}-\frac{22}{15}$$

Since \frac{3}{15} and \frac{22}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\Delta =\frac{3-22}{15}$$

Subtract 22 from 3 to get -19.

$$-\Delta =-\frac{19}{15}$$

Multiply both sides by -1.

$$\Delta =\frac{19}{15}$$