To solve the equation \( 7x + 66 = 122 \), follow these steps:

1. **Subtract 66 from both sides** to isolate the term with \( x \) on one side:
   \[
   7x + 66 - 66 = 122 - 66
   \]
   This simplifies to:
   \[
   7x = 56
   \]

2. **Divide both sides by 7** to solve for \( x \):
   \[
   x = \frac{56}{7}
   \]
   Simplifying:
   \[
   x = 8
   \]

So, the solution is \( x = 8 \).

Would you like more details, or do you have any questions?

Here are some related questions to practice:
1. Solve \( 5x + 12 = 37 \).
2. Solve \( 9x - 15 = 72 \).
3. Solve \( 3x + 27 = 81 \).
4. Solve \( 8x - 20 = 36 \).
5. Solve \( 6x + 44 = 88 \).

**Tip:** Always perform the same operation on both sides of the equation to maintain equality.

Learn how to solve the linear equation 7x + 66 = 122 with a clear, step-by-step solution. This problem demonstrates key algebraic concepts, including isolating variables and balancing equations. Suitable for students in Grades 6-8.

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