To solve for $x$ in the equation:

$-4x + 7 = -11$

we'll go through the following steps:

Step 1: Isolate the term with $x$

Subtract 7 from both sides of the equation to get: $-4x = -11 - 7$ $-4x = -18$

Step 2: Solve for $x$

Divide both sides by -4: $x = \frac{-18}{-4}$ $x = \frac{18}{4}$ $x = 4.5$

Answer

The correct answer is: $\boxed{E. \; 4.5}$

Would you like further explanation on solving linear equations or any other details?

Here are some related questions for practice:

1. If $-3x + 5 = 10$, what is $x$?
2. Solve for $x$ in $5x - 2 = 18$.
3. If $6x + 12 = 30$, what is $x$?
4. Solve $-2x + 9 = -3$ for $x$.
5. If $-5x + 8 = -7$, what is $x$?

Tip: Always perform the same operation on both sides of an equation to maintain balance and solve for the variable systematically.