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The problem asks us to solve the equation \( 3(x + 6) + 7 = 8(x - 7) \) for \( x \).

Let's solve it step by step.

1. **Distribute the constants:**
   \[
   3(x + 6) = 3x + 18
   \]
   \[
   8(x - 7) = 8x - 56
   \]
   Now the equation becomes:
   \[
   3x + 18 + 7 = 8x - 56
   \]

2. **Simplify both sides:**
   Combine like terms on the left side:
   \[
   3x + 25 = 8x - 56
   \]

3. **Move all terms involving \( x \) to one side and constants to the other:**
   Subtract \( 3x \) from both sides:
   \[
   25 = 5x - 56
   \]
   Add 56 to both sides:
   \[
   81 = 5x
   \]

4. **Solve for \( x \):**
   Divide both sides by 5:
   \[
   x = \frac{81}{5}
   \]

Thus, the solution is \( x = \frac{81}{5} \).

Would you like further explanation or details on any step?

### Related questions:
1. How do you handle equations with fractions?
2. What happens if we have variables on both sides of the equation?
3. How do you check if your solution is correct in equations like this?
4. What other methods could be used to solve linear equations?
5. What should you do if an equation contains parentheses with more complex expressions?

### Tip:
Always check your solution by substituting the value of \( x \) back into the original equation.

Solve 3(x + 6) + 7 = 8(x - 7) for x algebraically. If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal.

Learn how to solve the linear equation 3(x + 6) + 7 = 8(x - 7) step-by-step, applying the distributive property and combining like terms. This solution covers algebraic manipulation suitable for Grades 8-10.

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