Solve 2/3(9a+6)=20.2

$$\frac { 2 } { 3 } ( 9 a + 6 ) = 20.2$$

Solve for a

$$a=2.7$$

Steps for Solving Linear Equation

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$9a+6=20.2\times \frac{3}{2}$$

Convert decimal number 20.2 to fraction \frac{202}{10}. Reduce the fraction \frac{202}{10} to lowest terms by extracting and canceling out 2.

$$9a+6=\frac{101}{5}\times \frac{3}{2}$$

Multiply \frac{101}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$9a+6=\frac{101\times 3}{5\times 2}$$

Do the multiplications in the fraction \frac{101\times 3}{5\times 2}.

$$9a+6=\frac{303}{10}$$

Subtract 6 from both sides.

$$9a=\frac{303}{10}-6$$

Convert 6 to fraction \frac{60}{10}.

$$9a=\frac{303}{10}-\frac{60}{10}$$

Since \frac{303}{10} and \frac{60}{10} have the same denominator, subtract them by subtracting their numerators.

$$9a=\frac{303-60}{10}$$

Subtract 60 from 303 to get 243.

$$9a=\frac{243}{10}$$

Divide both sides by 9.

$$a=\frac{\frac{243}{10}}{9}$$

Express \frac{\frac{243}{10}}{9} as a single fraction.

$$a=\frac{243}{10\times 9}$$

Multiply 10 and 9 to get 90.

$$a=\frac{243}{90}$$

Reduce the fraction \frac{243}{90} to lowest terms by extracting and canceling out 9.

$$a=\frac{27}{10}$$