Solve Gamma=-(7/15-1)-3/5+1-5/3+(3/5-frac{11}{15})

$$\Gamma = - ( \frac { 7 } { 15 } - 1 ) - \frac { 3 } { 5 } + 1 - \frac { 5 } { 3 } + ( \frac { 3 } { 5 } - \frac { 11 } { 15 } )$$

Solve for Γ

$$\Gamma =-\frac{13}{15}\approx -0.866666667$$

Steps for Solving Linear Equation

Convert 1 to fraction \frac{15}{15}.

$$\Gamma =-\left(\frac{7}{15}-\frac{15}{15}\right)-\frac{3}{5}+1-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Since \frac{7}{15} and \frac{15}{15} have the same denominator, subtract them by subtracting their numerators.

$$\Gamma =-\frac{7-15}{15}-\frac{3}{5}+1-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Subtract 15 from 7 to get -8.

$$\Gamma =-\left(-\frac{8}{15}\right)-\frac{3}{5}+1-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

The opposite of -\frac{8}{15} is \frac{8}{15}.

$$\Gamma =\frac{8}{15}-\frac{3}{5}+1-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Least common multiple of 15 and 5 is 15. Convert \frac{8}{15} and \frac{3}{5} to fractions with denominator 15.

$$\Gamma =\frac{8}{15}-\frac{9}{15}+1-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Since \frac{8}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\Gamma =\frac{8-9}{15}+1-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Subtract 9 from 8 to get -1.

$$\Gamma =-\frac{1}{15}+1-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Convert 1 to fraction \frac{15}{15}.

$$\Gamma =-\frac{1}{15}+\frac{15}{15}-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Since -\frac{1}{15} and \frac{15}{15} have the same denominator, add them by adding their numerators.

$$\Gamma =\frac{-1+15}{15}-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Add -1 and 15 to get 14.

$$\Gamma =\frac{14}{15}-\frac{5}{3}+\frac{3}{5}-\frac{11}{15}$$

Least common multiple of 15 and 3 is 15. Convert \frac{14}{15} and \frac{5}{3} to fractions with denominator 15.

$$\Gamma =\frac{14}{15}-\frac{25}{15}+\frac{3}{5}-\frac{11}{15}$$

Since \frac{14}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\Gamma =\frac{14-25}{15}+\frac{3}{5}-\frac{11}{15}$$

Subtract 25 from 14 to get -11.

$$\Gamma =-\frac{11}{15}+\frac{3}{5}-\frac{11}{15}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{11}{15} and \frac{3}{5} to fractions with denominator 15.

$$\Gamma =-\frac{11}{15}+\frac{9}{15}-\frac{11}{15}$$

Since -\frac{11}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\Gamma =\frac{-11+9}{15}-\frac{11}{15}$$

Add -11 and 9 to get -2.

$$\Gamma =-\frac{2}{15}-\frac{11}{15}$$

Since -\frac{2}{15} and \frac{11}{15} have the same denominator, subtract them by subtracting their numerators.

$$\Gamma =\frac{-2-11}{15}$$

Subtract 11 from -2 to get -13.

$$\Gamma =-\frac{13}{15}$$

Assign Γ

$$\Gamma ≔-\frac{13}{15}$$