Multiply $ \dfrac{3}{8} $ by $ x $ to get $ \dfrac{ 3x }{ 8 } $.

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.

$$ \begin{aligned} \frac{3}{8} \cdot x & \xlongequal{\text{Step 1}} \frac{3}{8} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot x }{ 8 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 3x }{ 8 } \end{aligned} $$

Subtract $ \dfrac{3x}{8} $ from $ \dfrac{5}{8} $ to get $ \dfrac{-3x+5}{8} $.

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

$$ \begin{aligned} \frac{5}{8} - \frac{3x}{8} & = \frac{5}{\color{blue}{8}} - \frac{3x}{\color{blue}{8}} =\frac{ 5 - 3x }{ \color{blue}{ 8 }} = \\[1ex] &= \frac{-3x+5}{8} \end{aligned} $$