Multiply $2$ by $ \dfrac{i}{1} $ to get $ 2i$.

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.

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

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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Combine like terms:

$$ 3 \color{blue}{-2i} \color{blue}{-i} = \color{blue}{-3i} +3 $$

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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Combine like terms:

$$ -3i+ \color{blue}{3} + \color{blue}{3} = -3i+ \color{blue}{6} $$

Subtract $ \dfrac{7i}{2} $ from $ -3i+6 $ to get $ \dfrac{ \color{purple}{ -13i+12 } }{ 2 }$.

Step 1: Write $ -3i+6 $ 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 $\color{blue}{ 2 }$.

$$ \begin{aligned} -3i+6- \frac{7i}{2} & \xlongequal{\text{Step 1}} \frac{-3i+6}{\color{red}{1}} - \frac{7i}{2} = \frac{ \left( -3i+6 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} - \frac{ 7i }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -6i+12 } }{ 2 } - \frac{ \color{purple}{ 7i } }{ 2 }=\frac{ \color{purple}{ -13i+12 } }{ 2 } \end{aligned} $$

Subtract $3i$ from $ \dfrac{-13i+12}{2} $ to get $ \dfrac{ \color{purple}{ -19i+12 } }{ 2 }$.

Step 1: Write $ 3i $ 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 second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{-13i+12}{2} -3i & \xlongequal{\text{Step 1}} \frac{-13i+12}{2} - \frac{3i}{\color{red}{1}} = \frac{ -13i+12 }{ 2 } - \frac{ 3i \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -13i+12 } }{ 2 } - \frac{ \color{purple}{ 6i } }{ 2 }=\frac{ \color{purple}{ -19i+12 } }{ 2 } \end{aligned} $$