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

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

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

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

Add $ \dfrac{-i+14}{2} $ and $ 10i $ to get $ \dfrac{ \color{purple}{ 19i+14 } }{ 2 }$.

Step 1: Write $ 10i $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{-i+14}{2} +10i & \xlongequal{\text{Step 1}} \frac{-i+14}{2} + \frac{10i}{\color{red}{1}} = \frac{ -i+14 }{ 2 } + \frac{ 10i \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -i+14 } }{ 2 } + \frac{ \color{purple}{ 20i } }{ 2 }=\frac{ \color{purple}{ 19i+14 } }{ 2 } \end{aligned} $$