Use the distributive property.

Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.

Combine like terms

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

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

Remove 1 from denominator.

Add $ \dfrac{7x}{2} $ and $ 3 $ to get $ \dfrac{ \color{purple}{ 7x+6 } }{ 2 }$.

Step 1: Write $ 3 $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{7x}{2} +3 & \xlongequal{\text{Step 1}} \frac{7x}{2} + \frac{3}{\color{red}{1}} = \frac{ 7x }{ 2 } + \frac{ 3 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x } }{ 2 } + \frac{ \color{purple}{ 6 } }{ 2 }=\frac{ \color{purple}{ 7x+6 } }{ 2 } \end{aligned} $$

Remove 1 from denominator.

Subtract $7x$ from $ \dfrac{7x+6}{2} $ to get $ \dfrac{ \color{purple}{ -7x+6 } }{ 2 }$.

Step 1: Write $ 7x $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{7x+6}{2} -7x & \xlongequal{\text{Step 1}} \frac{7x+6}{2} - \frac{7x}{\color{red}{1}} = \frac{ 7x+6 }{ 2 } - \frac{ 7x \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x+6 } }{ 2 } - \frac{ \color{purple}{ 14x } }{ 2 }=\frac{ \color{purple}{ -7x+6 } }{ 2 } \end{aligned} $$

Remove 1 from denominator.

Subtract $2x$ from $ \dfrac{-7x+6}{2} $ to get $ \dfrac{ \color{purple}{ -11x+6 } }{ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{-7x+6}{2} -2x & \xlongequal{\text{Step 1}} \frac{-7x+6}{2} - \frac{2x}{\color{red}{1}} = \frac{ -7x+6 }{ 2 } - \frac{ 2x \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -7x+6 } }{ 2 } - \frac{ \color{purple}{ 4x } }{ 2 }=\frac{ \color{purple}{ -11x+6 } }{ 2 } \end{aligned} $$

Add $ \dfrac{-11x+6}{2} $ and $ 3 $ to get $ \dfrac{ \color{purple}{ -11x+12 } }{ 2 }$.

Step 1: Write $ 3 $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{-11x+6}{2} +3 & \xlongequal{\text{Step 1}} \frac{-11x+6}{2} + \frac{3}{\color{red}{1}} = \frac{ -11x+6 }{ 2 } + \frac{ 3 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -11x+6 } }{ 2 } + \frac{ \color{purple}{ 6 } }{ 2 }=\frac{ \color{purple}{ -11x+12 } }{ 2 } \end{aligned} $$