Solve [(21/3:31/2+5/9)-5/6]:2frac{1}{3}+frac{5}{6}=0.5p

$$[ ( 2 \frac { 1 } { 3 } : 3 \frac { 1 } { 2 } + \frac { 5 } { 9 } ) - \frac { 5 } { 6 } ] : 2 \frac { 1 } { 3 } + \frac { 5 } { 6 } = 0.5 p$$

Solve for p

$$p=2$$

Steps for Solving Linear Equation

Divide \frac{2\times 3+1}{3} by \frac{3\times 2+1}{2} by multiplying \frac{2\times 3+1}{3} by the reciprocal of \frac{3\times 2+1}{2}.

$$\frac{\frac{\left(2\times 3+1\right)\times 2}{3\left(3\times 2+1\right)}+\frac{5}{9}-\frac{5}{6}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Cancel out 1+2\times 3 in both numerator and denominator.

$$\frac{\frac{2}{3}+\frac{5}{9}-\frac{5}{6}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{5}{9} to fractions with denominator 9.

$$\frac{\frac{6}{9}+\frac{5}{9}-\frac{5}{6}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Since \frac{6}{9} and \frac{5}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6+5}{9}-\frac{5}{6}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Add 6 and 5 to get 11.

$$\frac{\frac{11}{9}-\frac{5}{6}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Least common multiple of 9 and 6 is 18. Convert \frac{11}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{\frac{22}{18}-\frac{15}{18}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Since \frac{22}{18} and \frac{15}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{22-15}{18}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Subtract 15 from 22 to get 7.

$$\frac{\frac{7}{18}}{\frac{2\times 3+1}{3}}+\frac{5}{6}=0.5p$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{7}{18}}{\frac{6+1}{3}}+\frac{5}{6}=0.5p$$

Add 6 and 1 to get 7.

$$\frac{\frac{7}{18}}{\frac{7}{3}}+\frac{5}{6}=0.5p$$

Divide \frac{7}{18} by \frac{7}{3} by multiplying \frac{7}{18} by the reciprocal of \frac{7}{3}.

$$\frac{7}{18}\times \frac{3}{7}+\frac{5}{6}=0.5p$$

Multiply \frac{7}{18} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{18\times 7}+\frac{5}{6}=0.5p$$

Cancel out 7 in both numerator and denominator.

$$\frac{3}{18}+\frac{5}{6}=0.5p$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}+\frac{5}{6}=0.5p$$

Since \frac{1}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+5}{6}=0.5p$$

Add 1 and 5 to get 6.

$$\frac{6}{6}=0.5p$$

Divide 6 by 6 to get 1.

$$1=0.5p$$

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

$$0.5p=1$$

Divide both sides by 0.5.

$$p=\frac{1}{0.5}$$

Expand \frac{1}{0.5} by multiplying both numerator and the denominator by 10.

$$p=\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$p=2$$