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

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.

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

Subtract $ \dfrac{7x}{4} $ from $ \dfrac{9}{4} $ to get $ \dfrac{-7x+9}{4} $.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{9}{4} - \frac{7x}{4} & = \frac{9}{\color{blue}{4}} - \frac{7x}{\color{blue}{4}} =\frac{ 9 - 7x }{ \color{blue}{ 4 }} = \\[1ex] &= \frac{-7x+9}{4} \end{aligned} $$