Multiply $4$ by $ \dfrac{x}{7} $ to get $ \dfrac{ 4x }{ 7 } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{x}{7} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{x}{7} \xlongequal{\text{Step 2}} \frac{ 4 \cdot x }{ 1 \cdot 7 } \xlongequal{\text{Step 3}} \frac{ 4x }{ 7 } \end{aligned} $$

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

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Cancel $ \color{blue}{ 2 } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

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

$$ 1 x x = x^{1 + 1} = x^2 $$

Subtract $x^2$ from $ \dfrac{4x}{7} $ to get $ \dfrac{ \color{purple}{ -7x^2+4x } }{ 7 }$.

Step 1: Write $ x^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 second fraction by $\color{blue}{7}$.

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

Add $ \dfrac{-7x^2+4x}{7} $ and $ 4 $ to get $ \dfrac{ \color{purple}{ -7x^2+4x+28 } }{ 7 }$.

Step 1: Write $ 4 $ 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 $\color{blue}{7}$.

$$ \begin{aligned} \frac{-7x^2+4x}{7} +4 & \xlongequal{\text{Step 1}} \frac{-7x^2+4x}{7} + \frac{4}{\color{red}{1}} = \frac{ -7x^2+4x }{ 7 } + \frac{ 4 \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -7x^2+4x } }{ 7 } + \frac{ \color{purple}{ 28 } }{ 7 }=\frac{ \color{purple}{ -7x^2+4x+28 } }{ 7 } \end{aligned} $$