Use the distributive property.

Multiply $4$ by $ \dfrac{i}{7} $ to get $ \dfrac{ 4i }{ 7 } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{i}{7} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{i}{7} \xlongequal{\text{Step 2}} \frac{ 4 \cdot i }{ 1 \cdot 7 } \xlongequal{\text{Step 3}} \frac{ 4i }{ 7 } \end{aligned} $$

Subtract $ \dfrac{i}{7} $ from $ \dfrac{1}{2} $ to get $ \dfrac{ \color{purple}{ -2i+7 } }{ 14 }$.

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

$$ \begin{aligned} \frac{1}{2} - \frac{i}{7} & = \frac{ 1 \cdot \color{blue}{ 7 }}{ 2 \cdot \color{blue}{ 7 }} - \frac{ i \cdot \color{blue}{ 2 }}{ 7 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 7 } }{ 14 } - \frac{ \color{purple}{ 2i } }{ 14 }=\frac{ \color{purple}{ -2i+7 } }{ 14 } \end{aligned} $$

Add $2$ and $ \dfrac{4i}{7} $ to get $ \dfrac{ \color{purple}{ 4i+14 } }{ 7 }$.

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 first fraction by $\color{blue}{ 7 }$.

$$ \begin{aligned} 2+ \frac{4i}{7} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} + \frac{4i}{7} = \frac{ 2 \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} + \frac{ 4i }{ 7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 14 } }{ 7 } + \frac{ \color{purple}{ 4i } }{ 7 }=\frac{ \color{purple}{ 4i+14 } }{ 7 } \end{aligned} $$

Multiply $ \dfrac{-2i+7}{14} $ by $ 5 $ to get $ \dfrac{ -10i+35 }{ 14 } $.

Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-2i+7}{14} \cdot 5 & \xlongequal{\text{Step 1}} \frac{-2i+7}{14} \cdot \frac{5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -2i+7 \right) \cdot 5 }{ 14 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -10i+35 }{ 14 } \end{aligned} $$

Add $2$ and $ \dfrac{4i}{7} $ to get $ \dfrac{ \color{purple}{ 4i+14 } }{ 7 }$.

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 first fraction by $\color{blue}{ 7 }$.

$$ \begin{aligned} 2+ \frac{4i}{7} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} + \frac{4i}{7} = \frac{ 2 \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} + \frac{ 4i }{ 7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 14 } }{ 7 } + \frac{ \color{purple}{ 4i } }{ 7 }=\frac{ \color{purple}{ 4i+14 } }{ 7 } \end{aligned} $$

Add $ \dfrac{-10i+35}{14} $ and $ \dfrac{4i+14}{7} $ to get $ \dfrac{ \color{purple}{ -2i+63 } }{ 14 }$.

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

$$ \begin{aligned} \frac{-10i+35}{14} + \frac{4i+14}{7} & = \frac{ -10i+35 }{ 14 } + \frac{ \left( 4i+14 \right) \cdot \color{blue}{ 2 }}{ 7 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -10i+35 } }{ 14 } + \frac{ \color{purple}{ 8i+28 } }{ 14 }=\frac{ \color{purple}{ -2i+63 } }{ 14 } \end{aligned} $$