Multiply $ \dfrac{8}{9} $ by $ x $ to get $ \dfrac{ 8x }{ 9 } $.

Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{8}{9} \cdot x & \xlongequal{\text{Step 1}} \frac{8}{9} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 8 \cdot x }{ 9 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 8x }{ 9 } \end{aligned} $$

Add $ \dfrac{2}{9} $ and $ \dfrac{8x}{9} $ to get $ \dfrac{8x+2}{9} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{2}{9} + \frac{8x}{9} & = \frac{2}{\color{blue}{9}} + \frac{8x}{\color{blue}{9}} =\frac{ 2 + 8x }{ \color{blue}{ 9 }} = \\[1ex] &= \frac{8x+2}{9} \end{aligned} $$