Solve -8/3+5/2x+19/7+13/5x=frac{118}{3}-frac{12}{7}

$$- \frac { 8 } { 3 } + \frac { 5 } { 2 } x + \frac { 19 } { 7 } + \frac { 13 } { 5 } x = \frac { 118 } { 3 } - \frac { 12 } { 7 }$$

Solve for x

$$x = \frac{2630}{357} = 7\frac{131}{357} \approx 7.366946779$$

Steps for Solving Linear Equation

Least common multiple of 3 and 7 is 21. Convert -\frac{8}{3} and \frac{19}{7} to fractions with denominator 21.

$$-\frac{56}{21}+\frac{5}{2}x+\frac{57}{21}+\frac{13}{5}x=\frac{118}{3}-\frac{12}{7}$$

Since -\frac{56}{21} and \frac{57}{21} have the same denominator, add them by adding their numerators.

$$\frac{-56+57}{21}+\frac{5}{2}x+\frac{13}{5}x=\frac{118}{3}-\frac{12}{7}$$

Add -56 and 57 to get 1.

$$\frac{1}{21}+\frac{5}{2}x+\frac{13}{5}x=\frac{118}{3}-\frac{12}{7}$$

Combine \frac{5}{2}x and \frac{13}{5}x to get \frac{51}{10}x.

$$\frac{1}{21}+\frac{51}{10}x=\frac{118}{3}-\frac{12}{7}$$

Least common multiple of 3 and 7 is 21. Convert \frac{118}{3} and \frac{12}{7} to fractions with denominator 21.

$$\frac{1}{21}+\frac{51}{10}x=\frac{826}{21}-\frac{36}{21}$$

Since \frac{826}{21} and \frac{36}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{21}+\frac{51}{10}x=\frac{826-36}{21}$$

Subtract 36 from 826 to get 790.

$$\frac{1}{21}+\frac{51}{10}x=\frac{790}{21}$$

Subtract \frac{1}{21} from both sides.

$$\frac{51}{10}x=\frac{790}{21}-\frac{1}{21}$$

Since \frac{790}{21} and \frac{1}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51}{10}x=\frac{790-1}{21}$$

Subtract 1 from 790 to get 789.

$$\frac{51}{10}x=\frac{789}{21}$$

Reduce the fraction \frac{789}{21} to lowest terms by extracting and canceling out 3.

$$\frac{51}{10}x=\frac{263}{7}$$

Multiply both sides by \frac{10}{51}, the reciprocal of \frac{51}{10}.

$$x=\frac{263}{7}\times \frac{10}{51}$$

Multiply \frac{263}{7} times \frac{10}{51} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{263\times 10}{7\times 51}$$

Do the multiplications in the fraction \frac{263\times 10}{7\times 51}.

$$x=\frac{2630}{357}$$