No problem. Let's solve the problem again with the corrected expression. 

The given information is that the average of \( x + 6 \), \( 6x + 2 \), and \( 2x + 7 \) is \( 4x - 7 \).

First, write the equation for the average of these three expressions:
\[
\frac{(x + 6) + (6x + 2) + (2x + 7)}{3} = 4x - 7
\]

Next, combine like terms in the numerator:
\[
\frac{x + 6 + 6x + 2 + 2x + 7}{3} = 4x - 7
\]

Simplify the numerator:
\[
\frac{(x + 6x + 2x) + (6 + 2 + 7)}{3} = 4x - 7
\]
\[
\frac{9x + 15}{3} = 4x - 7
\]

Now, divide both terms in the numerator by 3:
\[
3x + 5 = 4x - 7
\]

Subtract \( 3x \) from both sides to isolate \( x \):
\[
5 = 4x - 3x - 7
\]
\[
5 = x - 7
\]

Add 7 to both sides to solve for \( x \):
\[
x = 12
\]

Therefore, the value of \( x \) is:
\[
x = 12
\]

Would you like further details or have any questions?

Here are five more questions you can ask:
1. How do you solve simultaneous equations using substitution?
2. What is the quadratic formula and how is it derived?
3. Can you explain the concept of limits in calculus?
4. How do you find the area under a curve using integration?
5. What are the properties of logarithms and how are they applied in solving equations?

**Tip:** Always double-check the given problem and your initial setup to ensure you are solving the correct equations with the correct expressions.

Learn how to solve the average equation problem step-by-step. Understand the concepts of equations and algebraic simplification. Suitable for Grades 7-9.

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