To solve the equation \( 3(-4x - 1) + 3x + 5 = 11 \), follow these steps:

1. **Distribute** the 3 to the terms inside the parentheses:
   \[
   3(-4x) + 3(-1) + 3x + 5 = 11
   \]
   This simplifies to:
   \[
   -12x - 3 + 3x + 5 = 11
   \]

2. **Combine like terms** on the left side:
   \[
   (-12x + 3x) + (-3 + 5) = 11
   \]
   Simplifying further:
   \[
   -9x + 2 = 11
   \]

3. **Isolate** the variable \( x \) by subtracting 2 from both sides:
   \[
   -9x = 9
   \]

4. **Solve for** \( x \) by dividing both sides by -9:
   \[
   x = \frac{9}{-9} = -1
   \]

So, the solution is \( x = -1 \).

Would you like further details or have any questions?

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Here are 5 related questions to explore:

1. How would the solution change if the equation was \( 3(-4x - 1) + 3x + 5 = 15 \)?
2. Can you verify the solution by substituting \( x = -1 \) back into the original equation?
3. How does distributing a negative coefficient affect the equation?
4. What is the impact of combining like terms on both sides of an equation?
5. How can you solve a similar equation involving fractions?

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

Learn how to solve the equation 3(-4x - 1) + 3x + 5 = 11 step-by-step with a detailed solution. This problem covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 7-9.

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