To simplify the expression \(-\frac{4}{7} + \frac{2}{7}x - 14x + \frac{4}{7}\), we follow these steps:

1. Combine the constant terms: \(-\frac{4}{7}\) and \(\frac{4}{7}\).
2. Combine the variable terms: \(\frac{2}{7}x\) and \(-14x\).

Let's proceed step-by-step.

### Step 1: Combine Constant Terms
\[
-\frac{4}{7} + \frac{4}{7} = 0
\]

### Step 2: Combine Variable Terms
\[
\frac{2}{7}x - 14x
\]

To combine these, we need a common denominator. Note that \(-14x\) can be written as \(-\frac{98}{7}x\) because \(-14 = -\frac{98}{7}\).

So,
\[
\frac{2}{7}x - \frac{98}{7}x = \left( \frac{2 - 98}{7} \right)x = -\frac{96}{7}x
\]

Thus, the simplified form of the expression is:
\[
-\frac{96}{7}x
\]

If you have any questions or need more details, feel free to ask!

Here are 5 related questions for further exploration:

1. How do you combine fractions with different denominators?
2. What is the process for simplifying algebraic expressions with multiple terms?
3. How can you convert whole numbers into fractions for easy combination?
4. What are the common mistakes to avoid when combining like terms?
5. How do you solve equations involving fractions and variables?

**Tip:** Always look for common denominators when combining fractions to simplify the process.

Learn how to simplify the algebraic expression -4/7 + 2/7x - 14x + 4/7 step-by-step. This problem demonstrates key algebraic concepts like combining like terms and working with fractions. Suitable for students in Grades 6-8.

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