We are given the equation:

\[
69 - 2x = 133 - 10x
\]

### Steps to solve for \( x \):

1. **Move all terms with \( x \) to one side**:
   Add \( 10x \) to both sides:

   \[
   69 - 2x + 10x = 133
   \]
   Simplifying:

   \[
   69 + 8x = 133
   \]

2. **Move the constants to the other side**:
   Subtract \( 69 \) from both sides:

   \[
   8x = 133 - 69
   \]
   Simplifying:

   \[
   8x = 64
   \]

3. **Solve for \( x \)**:
   Divide both sides by 8:

   \[
   x = \frac{64}{8}
   \]
   Simplifying:

   \[
   x = 8
   \]

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

Would you like further details or have any questions?

Here are 5 related questions to extend your learning:

1. What happens if you change the constant on the right side of the equation?
2. How would you approach solving \( 5x - 7 = 2x + 21 \)?
3. Can you solve an equation where the variable \( x \) appears in the denominator?
4. How does solving inequalities differ from solving equations?
5. What is the graphical interpretation of solving this equation?

**Tip**: When solving equations, always simplify step-by-step to avoid mistakes.

Learn how to solve the linear equation 69 - 2x = 133 - 10x with step-by-step explanations. This solution covers essential algebra concepts such as moving terms with variables and constants to one side and simplifying. Ideal for students in Grades 6-8.

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