The equation you have provided is:

$-4x + 3 = -11$

To solve for $x$, follow these steps:

1. Subtract 3 from both sides to eliminate the constant on the left: $-4x = -11 - 3$ $-4x = -14$

2. Divide both sides by -4 to solve for $x$: $x = \frac{-14}{-4}$ $x = \frac{14}{4} = 3.5$

So, the solution is: $x = 3.5$

Would you like more details, or do you have any questions?

Here are 5 related questions to explore further:

1. What happens when the coefficient of $x$ is positive instead of negative?
2. How do you solve a similar equation if fractions are involved from the start?
3. How do we check if our solution is correct in equations?
4. What changes in solving equations if you deal with inequalities instead of equalities?
5. How would you solve an equation like $-4x + 3 = 11$ (positive right side)?

Tip: Always perform inverse operations to isolate the variable step by step!