Use the distributive property.

Multiply $ \dfrac{5}{4} $ by $ x $ to get $ \dfrac{ 5x }{ 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.

$$ \begin{aligned} \frac{5}{4} \cdot x & \xlongequal{\text{Step 1}} \frac{5}{4} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 4 } \end{aligned} $$

Combine like terms

Multiply $ \dfrac{5}{4} $ by $ x $ to get $ \dfrac{ 5x }{ 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.

$$ \begin{aligned} \frac{5}{4} \cdot x & \xlongequal{\text{Step 1}} \frac{5}{4} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 4 } \end{aligned} $$

Combine like terms:

$$ \color{blue}{9x} \color{blue}{-15x} = \color{blue}{-6x} $$

Subtract $ \dfrac{5x}{4} $ from $ -6x $ to get $ \dfrac{ \color{purple}{ -29x } }{ 4 }$.

Step 1: Write $ -6x $ 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 $\color{blue}{ 4 }$.

$$ \begin{aligned} -6x- \frac{5x}{4} & \xlongequal{\text{Step 1}} \frac{-6x}{\color{red}{1}} - \frac{5x}{4} = \frac{ \left( -6x \right) \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} - \frac{ 5x }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -24x } }{ 4 } - \frac{ \color{purple}{ 5x } }{ 4 }=\frac{ \color{purple}{ -29x } }{ 4 } \end{aligned} $$

Add $ \dfrac{-29x}{4} $ and $ 6 $ to get $ \dfrac{ \color{purple}{ -29x+24 } }{ 4 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{-29x}{4} +6 & \xlongequal{\text{Step 1}} \frac{-29x}{4} + \frac{6}{\color{red}{1}} = \frac{ -29x }{ 4 } + \frac{ 6 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -29x } }{ 4 } + \frac{ \color{purple}{ 24 } }{ 4 }=\frac{ \color{purple}{ -29x+24 } }{ 4 } \end{aligned} $$