Solve (-7/5-9/2)=K(-9/5-5/2)

$$( - \frac { 7 } { 5 } - \frac { 9 } { 2 } ) = K ( - \frac { 9 } { 5 } - \frac { 5 } { 2 } )$$

Solve for K

$$K = \frac{59}{43} = 1\frac{16}{43} \approx 1.372093023$$

Steps for Solving Linear Equation

Least common multiple of 5 and 2 is 10. Convert -\frac{7}{5} and \frac{9}{2} to fractions with denominator 10.

$$-\frac{14}{10}-\frac{45}{10}=K\left(-\frac{9}{5}-\frac{5}{2}\right)$$

Since -\frac{14}{10} and \frac{45}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-14-45}{10}=K\left(-\frac{9}{5}-\frac{5}{2}\right)$$

Subtract 45 from -14 to get -59.

$$-\frac{59}{10}=K\left(-\frac{9}{5}-\frac{5}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert -\frac{9}{5} and \frac{5}{2} to fractions with denominator 10.

$$-\frac{59}{10}=K\left(-\frac{18}{10}-\frac{25}{10}\right)$$

Since -\frac{18}{10} and \frac{25}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{59}{10}=K\times \frac{-18-25}{10}$$

Subtract 25 from -18 to get -43.

$$-\frac{59}{10}=K\left(-\frac{43}{10}\right)$$

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

$$K\left(-\frac{43}{10}\right)=-\frac{59}{10}$$

Multiply both sides by -\frac{10}{43}, the reciprocal of -\frac{43}{10}.

$$K=-\frac{59}{10}\left(-\frac{10}{43}\right)$$

Multiply -\frac{59}{10} times -\frac{10}{43} by multiplying numerator times numerator and denominator times denominator.

$$K=\frac{-59\left(-10\right)}{10\times 43}$$

Do the multiplications in the fraction \frac{-59\left(-10\right)}{10\times 43}.

$$K=\frac{590}{430}$$

Reduce the fraction \frac{590}{430} to lowest terms by extracting and canceling out 10.

$$K=\frac{59}{43}$$