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To solve the equation:

\[
-4x + 7 = -11
\]

we will isolate \( x \) by following these steps:

1. **Subtract 7 from both sides**:
   \[
   -4x = -11 - 7
   \]
   \[
   -4x = -18
   \]

2. **Divide both sides by -4** to solve for \( x \):
   \[
   x = \frac{-18}{-4} = \frac{18}{4} = 4.5
   \]

Thus, the answer is:
\[
\boxed{\text{E. } 4.5}
\]

Would you like a further breakdown of the steps? Here are some additional questions that build on this type of problem:

1. How would the solution change if the equation were \( -4x + 7 = -13 \)?
2. What is the solution if the equation is \( -5x + 7 = -18 \)?
3. How can you check if a solution is correct in a linear equation?
4. If the equation were \( 4x - 7 = 11 \), what would be the value of \( x \)?
5. How does changing the sign of \( x \) in the equation affect the solution?

**Tip:** When solving linear equations, always perform the same operation on both sides to keep the equation balanced.

Learn how to solve the linear equation -4x + 7 = -11 with a step-by-step solution. This problem covers key algebraic concepts, focusing on solving for a variable in a simple linear equation. Suitable for students in Grades 7-9.

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