Solve x-5/frac{7{5}-5}=4-1/-frac{4{5}-1}

$$\frac { x - 5 } { \frac { 7 } { 5 } - 5 } = \frac { 4 - 1 } { - \frac { 4 } { 5 } - 1 }$$

Solve for x

$$x=11$$

Steps for Solving Linear Equation

Convert 5 to fraction \frac{25}{5}.

$$\frac{x-5}{\frac{7}{5}-\frac{25}{5}}=\frac{4-1}{-\frac{4}{5}-1}$$

Since \frac{7}{5} and \frac{25}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-5}{\frac{7-25}{5}}=\frac{4-1}{-\frac{4}{5}-1}$$

Subtract 25 from 7 to get -18.

$$\frac{x-5}{-\frac{18}{5}}=\frac{4-1}{-\frac{4}{5}-1}$$

Multiply both numerator and denominator by -1.

$$\frac{-x+5}{\frac{18}{5}}=\frac{4-1}{-\frac{4}{5}-1}$$

Subtract 1 from 4 to get 3.

$$\frac{-x+5}{\frac{18}{5}}=\frac{3}{-\frac{4}{5}-1}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{-x+5}{\frac{18}{5}}=\frac{3}{-\frac{4}{5}-\frac{5}{5}}$$

Since -\frac{4}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x+5}{\frac{18}{5}}=\frac{3}{\frac{-4-5}{5}}$$

Subtract 5 from -4 to get -9.

$$\frac{-x+5}{\frac{18}{5}}=\frac{3}{-\frac{9}{5}}$$

Divide 3 by -\frac{9}{5} by multiplying 3 by the reciprocal of -\frac{9}{5}.

$$\frac{-x+5}{\frac{18}{5}}=3\left(-\frac{5}{9}\right)$$

Express 3\left(-\frac{5}{9}\right) as a single fraction.

$$\frac{-x+5}{\frac{18}{5}}=\frac{3\left(-5\right)}{9}$$

Multiply 3 and -5 to get -15.

$$\frac{-x+5}{\frac{18}{5}}=\frac{-15}{9}$$

Reduce the fraction \frac{-15}{9} to lowest terms by extracting and canceling out 3.

$$\frac{-x+5}{\frac{18}{5}}=-\frac{5}{3}$$

Divide each term of -x+5 by \frac{18}{5} to get \frac{-x}{\frac{18}{5}}+\frac{5}{\frac{18}{5}}.

$$\frac{-x}{\frac{18}{5}}+\frac{5}{\frac{18}{5}}=-\frac{5}{3}$$

Divide -x by \frac{18}{5} to get -\frac{5}{18}x.

$$-\frac{5}{18}x+\frac{5}{\frac{18}{5}}=-\frac{5}{3}$$

Divide 5 by \frac{18}{5} by multiplying 5 by the reciprocal of \frac{18}{5}.

$$-\frac{5}{18}x+5\times \frac{5}{18}=-\frac{5}{3}$$

Express 5\times \frac{5}{18} as a single fraction.

$$-\frac{5}{18}x+\frac{5\times 5}{18}=-\frac{5}{3}$$

Multiply 5 and 5 to get 25.

$$-\frac{5}{18}x+\frac{25}{18}=-\frac{5}{3}$$

Subtract \frac{25}{18} from both sides.

$$-\frac{5}{18}x=-\frac{5}{3}-\frac{25}{18}$$

Least common multiple of 3 and 18 is 18. Convert -\frac{5}{3} and \frac{25}{18} to fractions with denominator 18.

$$-\frac{5}{18}x=-\frac{30}{18}-\frac{25}{18}$$

Since -\frac{30}{18} and \frac{25}{18} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{18}x=\frac{-30-25}{18}$$

Subtract 25 from -30 to get -55.

$$-\frac{5}{18}x=-\frac{55}{18}$$

Multiply both sides by -\frac{18}{5}, the reciprocal of -\frac{5}{18}.

$$x=-\frac{55}{18}\left(-\frac{18}{5}\right)$$

Multiply -\frac{55}{18} times -\frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-55\left(-18\right)}{18\times 5}$$

Do the multiplications in the fraction \frac{-55\left(-18\right)}{18\times 5}.

$$x=\frac{990}{90}$$

Divide 990 by 90 to get 11.

$$x=11$$