Let's solve the equation:

$2x \cdot 2 + 9x - 1 = 2x - 7$

Step 1: Simplify both sides

On the left side: $2x \cdot 2 = 4x$ So, the equation becomes: $4x + 9x - 1 = 2x - 7$

Step 2: Combine like terms

On the left side, combine $4x$ and $9x$: $13x - 1 = 2x - 7$

Step 3: Move all $x$-terms to one side

Subtract $2x$ from both sides: $13x - 2x - 1 = -7$ $11x - 1 = -7$

Step 4: Solve for $x$

Add 1 to both sides: $11x = -6$ Now, divide both sides by 11: $x = \frac{-6}{11}$

Final Answer:

$x = \frac{-6}{11}$

Let me know if you need more details or have any questions!

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Here are 5 related questions you might explore:

1. What happens if we modify the constants in the equation slightly, such as replacing $9x$ with $10x$?
2. How would you handle an equation with fractions instead of whole numbers?
3. Can you apply these steps to solve the quadratic equation $x^2 - 4x + 4 = 0$?
4. How would the solution change if the equation involved exponents?
5. What if the equation were $2x^2 + 9x - 1 = 2x - 7$? How would you solve it?

Tip: Always remember to check your final solution by substituting the value of $x$ back into the original equation!