Multiply $3$ by $ \dfrac{x}{2} $ to get $ \dfrac{ 3x }{ 2 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $2x$ from $ \dfrac{3x}{2} $ to get $ \dfrac{ \color{purple}{ -x } }{ 2 }$.

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

$$ \begin{aligned} \frac{3x}{2} -2x & \xlongequal{\text{Step 1}} \frac{3x}{2} - \frac{2x}{\color{red}{1}} = \frac{ 3x }{ 2 } - \frac{ 2x \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x } }{ 2 } - \frac{ \color{purple}{ 4x } }{ 2 }=\frac{ \color{purple}{ -x } }{ 2 } \end{aligned} $$

Subtract $ \dfrac{1}{3} $ from $ \dfrac{-x}{2} $ to get $ \dfrac{ \color{purple}{ -3x-2 } }{ 6 }$.

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}{ 3 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{-x}{2} - \frac{1}{3} & = \frac{ \left( -x \right) \cdot \color{blue}{ 3 }}{ 2 \cdot \color{blue}{ 3 }} - \frac{ 1 \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -3x } }{ 6 } - \frac{ \color{purple}{ 2 } }{ 6 }=\frac{ \color{purple}{ -3x-2 } }{ 6 } \end{aligned} $$