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

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

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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7x}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{7x}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7x \cdot x }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7x^2 }{ 2 } \end{aligned} $$

Subtract $ \dfrac{7x^2}{2} $ from $ 2x^2 $ to get $ \dfrac{ \color{purple}{ -3x^2 } }{ 2 }$.

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

$$ \begin{aligned} 2x^2- \frac{7x^2}{2} & \xlongequal{\text{Step 1}} \frac{2x^2}{\color{red}{1}} - \frac{7x^2}{2} = \frac{ 2x^2 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} - \frac{ 7x^2 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^2 } }{ 2 } - \frac{ \color{purple}{ 7x^2 } }{ 2 }=\frac{ \color{purple}{ -3x^2 } }{ 2 } \end{aligned} $$

Subtract $7$ from $ \dfrac{-3x^2}{2} $ to get $ \dfrac{ \color{purple}{ -3x^2-14 } }{ 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 second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{-3x^2}{2} -7 & \xlongequal{\text{Step 1}} \frac{-3x^2}{2} - \frac{7}{\color{red}{1}} = \frac{ -3x^2 }{ 2 } - \frac{ 7 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -3x^2 } }{ 2 } - \frac{ \color{purple}{ 14 } }{ 2 }=\frac{ \color{purple}{ -3x^2-14 } }{ 2 } \end{aligned} $$