We are given the following expression:

\[
\frac{1}{14} \left(\frac{5x + 4x - 7}{2}\right) - 8x
\]

Let's simplify this step-by-step.

### Step 1: Combine like terms inside the parentheses.
First, combine the like terms \(5x\) and \(4x\):

\[
5x + 4x = 9x
\]

Now the expression becomes:

\[
\frac{1}{14} \left(\frac{9x - 7}{2}\right) - 8x
\]

### Step 2: Simplify the fraction inside the parentheses.
Distribute the \( \frac{1}{2} \) across the terms in the numerator:

\[
\frac{9x - 7}{2} = \frac{9x}{2} - \frac{7}{2}
\]

Now the expression is:

\[
\frac{1}{14} \left( \frac{9x}{2} - \frac{7}{2} \right) - 8x
\]

### Step 3: Distribute \(\frac{1}{14}\) to both terms.
We distribute \(\frac{1}{14}\) to both \(\frac{9x}{2}\) and \(\frac{7}{2}\):

\[
\frac{1}{14} \times \frac{9x}{2} = \frac{9x}{28}, \quad \frac{1}{14} \times \frac{7}{2} = \frac{7}{28} = \frac{1}{4}
\]

Thus, the expression becomes:

\[
\frac{9x}{28} - \frac{1}{4} - 8x
\]

### Step 4: Simplify the expression.
Now we can combine the terms:

1. Convert \(-8x\) to have the same denominator as \(\frac{9x}{28}\). \(-8x = \frac{-224x}{28}\).

Now the expression becomes:

\[
\frac{9x}{28} - \frac{224x}{28} - \frac{1}{4}
\]

2. Combine the terms with \(x\):

\[
\frac{9x - 224x}{28} = \frac{-215x}{28}
\]

So the expression is now:

\[
\frac{-215x}{28} - \frac{1}{4}
\]

This is the simplified form of the given expression.

Would you like more details or have any questions?

### Related Questions:
1. How do you solve similar problems involving fractions and algebraic terms?
2. What is the process of distributing fractions in algebraic expressions?
3. How do you handle combining terms with different denominators?
4. How do you simplify expressions involving multiple fractions?
5. Can you give an example where fractions and variables are combined differently?

### Tip:
When simplifying expressions with fractions, always look for opportunities to combine like terms and reduce the complexity by finding a common denominator.

Learn how to simplify the algebraic expression 1/14 (5x + 4x - 7/2) - 8x through step-by-step combination of like terms, fraction simplification, and distributing fractions. This problem is suitable for students in Grades 8-10 and covers key algebraic concepts.

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