Multiply $2$ by $ \dfrac{i}{7} $ to get $ \dfrac{ 2i }{ 7 } $.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{i}{7} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{7} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 7 } \xlongequal{\text{Step 3}} \frac{ 2i }{ 7 } \end{aligned} $$

Multiply $9$ by $ \dfrac{i}{2} $ to get $ \dfrac{ 9i }{ 2 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $9$ by $ \dfrac{i}{14} $ to get $ \dfrac{ 9i }{ 14 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 9 \cdot \frac{i}{14} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{i}{14} \xlongequal{\text{Step 2}} \frac{ 9 \cdot i }{ 1 \cdot 14 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9i }{ 14 } \end{aligned} $$

Add $ \dfrac{-2i}{7} $ and $ 7 $ to get $ \dfrac{ \color{purple}{ -2i+49 } }{ 7 }$.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{7}$.

$$ \begin{aligned} \frac{-2i}{7} +7 & \xlongequal{\text{Step 1}} \frac{-2i}{7} + \frac{7}{\color{red}{1}} = \frac{ -2i }{ 7 } + \frac{ 7 \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2i } }{ 7 } + \frac{ \color{purple}{ 49 } }{ 7 }=\frac{ \color{purple}{ -2i+49 } }{ 7 } \end{aligned} $$

Multiply $9$ by $ \dfrac{i}{2} $ to get $ \dfrac{ 9i }{ 2 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $9$ by $ \dfrac{i}{14} $ to get $ \dfrac{ 9i }{ 14 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 9 \cdot \frac{i}{14} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{i}{14} \xlongequal{\text{Step 2}} \frac{ 9 \cdot i }{ 1 \cdot 14 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9i }{ 14 } \end{aligned} $$

Add $ \dfrac{-2i+49}{7} $ and $ \dfrac{9i}{2} $ to get $ \dfrac{ \color{purple}{ 59i+98 } }{ 14 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 2 }$ and the second by $\color{blue}{ 7 }$.

$$ \begin{aligned} \frac{-2i+49}{7} + \frac{9i}{2} & = \frac{ \left( -2i+49 \right) \cdot \color{blue}{ 2 }}{ 7 \cdot \color{blue}{ 2 }} + \frac{ 9i \cdot \color{blue}{ 7 }}{ 2 \cdot \color{blue}{ 7 }} = \\[1ex] &=\frac{ \color{purple}{ -4i+98 } }{ 14 } + \frac{ \color{purple}{ 63i } }{ 14 }=\frac{ \color{purple}{ 59i+98 } }{ 14 } \end{aligned} $$

Multiply $9$ by $ \dfrac{i}{14} $ to get $ \dfrac{ 9i }{ 14 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 9 \cdot \frac{i}{14} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{i}{14} \xlongequal{\text{Step 2}} \frac{ 9 \cdot i }{ 1 \cdot 14 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9i }{ 14 } \end{aligned} $$

Add $ \dfrac{59i+98}{14} $ and $ 2 $ to get $ \dfrac{ \color{purple}{ 59i+126 } }{ 14 }$.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{14}$.

$$ \begin{aligned} \frac{59i+98}{14} +2 & \xlongequal{\text{Step 1}} \frac{59i+98}{14} + \frac{2}{\color{red}{1}} = \frac{ 59i+98 }{ 14 } + \frac{ 2 \cdot \color{blue}{ 14 }}{ 1 \cdot \color{blue}{ 14 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 59i+98 } }{ 14 } + \frac{ \color{purple}{ 28 } }{ 14 }=\frac{ \color{purple}{ 59i+126 } }{ 14 } \end{aligned} $$

Multiply $9$ by $ \dfrac{i}{14} $ to get $ \dfrac{ 9i }{ 14 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 9 \cdot \frac{i}{14} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{i}{14} \xlongequal{\text{Step 2}} \frac{ 9 \cdot i }{ 1 \cdot 14 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9i }{ 14 } \end{aligned} $$

Subtract $ \dfrac{9i}{14} $ from $ \dfrac{59i+126}{14} $ to get $ \dfrac{50i+126}{14} $.

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

$$ \begin{aligned} \frac{59i+126}{14} - \frac{9i}{14} & = \frac{59i+126}{\color{blue}{14}} - \frac{9i}{\color{blue}{14}} =\frac{ 59i+126 - 9i }{ \color{blue}{ 14 }} = \\[1ex] &= \frac{50i+126}{14} \end{aligned} $$