Solve 1/2b-19/10=1/3b+5/6

$$\frac { 1 } { 2 } b - \frac { 19 } { 10 } = \frac { 1 } { 3 } b + \frac { 5 } { 6 }$$

Solve for b

$$b = \frac{82}{5} = 16\frac{2}{5} = 16.4$$

Steps for Solving Linear Equation

Subtract \frac{1}{3}b from both sides.

$$\frac{1}{2}b-\frac{19}{10}-\frac{1}{3}b=\frac{5}{6}$$

Combine \frac{1}{2}b and -\frac{1}{3}b to get \frac{1}{6}b.

$$\frac{1}{6}b-\frac{19}{10}=\frac{5}{6}$$

Add \frac{19}{10} to both sides.

$$\frac{1}{6}b=\frac{5}{6}+\frac{19}{10}$$

Least common multiple of 6 and 10 is 30. Convert \frac{5}{6} and \frac{19}{10} to fractions with denominator 30.

$$\frac{1}{6}b=\frac{25}{30}+\frac{57}{30}$$

Since \frac{25}{30} and \frac{57}{30} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}b=\frac{25+57}{30}$$

Add 25 and 57 to get 82.

$$\frac{1}{6}b=\frac{82}{30}$$

Reduce the fraction \frac{82}{30} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}b=\frac{41}{15}$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}.

$$b=\frac{41}{15}\times 6$$

Express \frac{41}{15}\times 6 as a single fraction.

$$b=\frac{41\times 6}{15}$$

Multiply 41 and 6 to get 246.

$$b=\frac{246}{15}$$

Reduce the fraction \frac{246}{15} to lowest terms by extracting and canceling out 3.

$$b=\frac{82}{5}$$