Let's solve the equation:

$-4(7 + 2x) = 7(x + 11)$

Step 1: Expand both sides of the equation

On the left-hand side, apply the distributive property:

$-4(7) - 4(2x) = -28 - 8x$

On the right-hand side, apply the distributive property as well:

$7(x) + 7(11) = 7x + 77$

Now, the equation becomes:

$-28 - 8x = 7x + 77$

Step 2: Move all terms with $x$ to one side

Add $8x$ to both sides to eliminate the $-8x$ from the left-hand side:

$-28 = 15x + 77$

Step 3: Move constant terms to the other side

Subtract 77 from both sides to isolate the term with $x$:

$-28 - 77 = 15x$

$-105 = 15x$

Step 4: Solve for $x$

Divide both sides by 15:

$x = \frac{-105}{15}$

$x = -7$

Final Answer:

$x = -7$

Do you have any questions or need further details?

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Here are 5 related questions to deepen your understanding:

1. What is the distributive property and how is it applied in algebraic equations?
2. How would the equation change if the right-hand side had been $7(x - 11)$?
3. Can you solve for $x$ if both sides of the equation included quadratic terms?
4. How would the solution differ if the original equation had different coefficients?
5. What would happen if you added a constant term to both sides of the equation?

Tip: Always double-check your work by substituting the solution back into the original equation to verify it.