# Question #ed141

Dec 2, 2016

$x = \frac{81}{16}$

#### Explanation:

$\frac{2}{3} x = \frac{27}{8}$

The term containing $x$ is isolated. Its coefficient is $\frac{2}{3}$. Multiply by $\frac{3}{2}$, the reciprocal of $\frac{2}{3}$, to isolate $x$.

$\frac{2}{3} x \times \frac{3}{2} = \frac{27}{8} \times \frac{3}{2}$

Use the commutative and associative properties of multiplication to group the reciprocal with the coefficient.

$\left(\frac{2}{3} \times \frac{3}{2}\right) x = \frac{27}{8} \times \frac{3}{2}$

When multiplying fractions, we follow $\frac{a}{b} \times \frac{c}{d} = \frac{a c}{b d}$

$\frac{2 \times 3}{3 \times 2} x = \frac{27 \times 3}{8 \times 2}$

$\implies \frac{6}{6} x = \frac{81}{16}$

$\implies 1 x = \frac{81}{16}$

$\therefore x = \frac{81}{16}$