To solve the equation \( 176 = 13(2 + 6x) - 6(x - 10) \), we need to expand and simplify both sides and then solve for \( x \).

1. Start by expanding both terms on the right side of the equation:
   \[
   176 = 13(2 + 6x) - 6(x - 10)
   \]

2. Distribute the 13 and -6:
   \[
   176 = 13 \cdot 2 + 13 \cdot 6x - 6 \cdot x + 6 \cdot 10
   \]
   \[
   176 = 26 + 78x - 6x + 60
   \]

3. Combine like terms on the right side:
   \[
   176 = 26 + 60 + (78x - 6x)
   \]
   \[
   176 = 86 + 72x
   \]

4. Subtract 86 from both sides to isolate the term with \( x \):
   \[
   176 - 86 = 72x
   \]
   \[
   90 = 72x
   \]

5. Finally, divide both sides by 72 to solve for \( x \):
   \[
   x = \frac{90}{72} = \frac{5}{4} = 1.25
   \]

So, the solution is \( x = 1.25 \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What happens if you substitute \( x = 1.25 \) back into the original equation?
2. How would the solution change if the coefficient of \( x \) in the second term were different?
3. Can you derive an alternative method to solve this equation?
4. How do you solve similar equations that involve quadratic terms?
5. What are the implications if \( x \) was required to be an integer?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 176 = 13(2 + 6x) - 6(x - 10) step-by-step. This problem involves linear equations and the distributive property, suitable for Grades 7-9.

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