Solve I=-3/5(2/3+5/4)-7/2(frac{4}{14}-frac{5}{7}))

$$I = - \frac { 3 } { 5 } ( \frac { 2 } { 3 } + \frac { 5 } { 4 } ) - \frac { 7 } { 2 } ( \frac { 4 } { 14 } - \frac { 5 } { 7 } ) )$$

Solve for I

$$I=\frac{7}{20}=0.35$$

Steps for Solving Linear Equation

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{5}{4} to fractions with denominator 12.

$$I=-\frac{3}{5}\left(\frac{8}{12}+\frac{15}{12}\right)-\frac{7}{2}\left(\frac{4}{14}-\frac{5}{7}\right)$$

Since \frac{8}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$I=-\frac{3}{5}\times \frac{8+15}{12}-\frac{7}{2}\left(\frac{4}{14}-\frac{5}{7}\right)$$

Add 8 and 15 to get 23.

$$I=-\frac{3}{5}\times \frac{23}{12}-\frac{7}{2}\left(\frac{4}{14}-\frac{5}{7}\right)$$

Multiply -\frac{3}{5} times \frac{23}{12} by multiplying numerator times numerator and denominator times denominator.

$$I=\frac{-3\times 23}{5\times 12}-\frac{7}{2}\left(\frac{4}{14}-\frac{5}{7}\right)$$

Do the multiplications in the fraction \frac{-3\times 23}{5\times 12}.

$$I=\frac{-69}{60}-\frac{7}{2}\left(\frac{4}{14}-\frac{5}{7}\right)$$

Reduce the fraction \frac{-69}{60} to lowest terms by extracting and canceling out 3.

$$I=-\frac{23}{20}-\frac{7}{2}\left(\frac{4}{14}-\frac{5}{7}\right)$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$I=-\frac{23}{20}-\frac{7}{2}\left(\frac{2}{7}-\frac{5}{7}\right)$$

Since \frac{2}{7} and \frac{5}{7} have the same denominator, subtract them by subtracting their numerators.

$$I=-\frac{23}{20}-\frac{7}{2}\times \frac{2-5}{7}$$

Subtract 5 from 2 to get -3.

$$I=-\frac{23}{20}-\frac{7}{2}\left(-\frac{3}{7}\right)$$

Multiply \frac{7}{2} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$I=-\frac{23}{20}-\frac{7\left(-3\right)}{2\times 7}$$

Cancel out 7 in both numerator and denominator.

$$I=-\frac{23}{20}-\frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$I=-\frac{23}{20}-\left(-\frac{3}{2}\right)$$

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

$$I=-\frac{23}{20}+\frac{3}{2}$$

Least common multiple of 20 and 2 is 20. Convert -\frac{23}{20} and \frac{3}{2} to fractions with denominator 20.

$$I=-\frac{23}{20}+\frac{30}{20}$$

Since -\frac{23}{20} and \frac{30}{20} have the same denominator, add them by adding their numerators.

$$I=\frac{-23+30}{20}$$

Add -23 and 30 to get 7.

$$I=\frac{7}{20}$$

Assign I

$$I≔\frac{7}{20}$$