To solve the equation \(-4x - 5 = -5x - 1\), let's first simplify and isolate the variable \(x\).

### Step-by-step Solution:

1. **Move all \(x\)-terms to one side**: To do this, add \(5x\) to both sides of the equation:

   \[
   -4x + 5x - 5 = -5x + 5x - 1
   \]

   Simplifying this gives:

   \[
   x - 5 = -1
   \]

2. **Isolate \(x\)**: Add 5 to both sides to isolate \(x\):

   \[
   x - 5 + 5 = -1 + 5
   \]

   This simplifies to:

   \[
   x = 4
   \]

### Solution:
The value of \(x\) is \(4\).

Would you like a more detailed explanation or have any questions? Here are some related questions to further explore:

1. How would the solution change if the equation was \(4x - 5 = 5x - 1\)?
2. What if both sides of the equation had additional terms, like \( -4x - 5 + 2y = -5x - 1 + y\)?
3. How do you solve an equation with fractions, such as \(\frac{-4x - 5}{2} = \frac{-5x - 1}{3}\)?
4. What happens when you have quadratic terms in an equation, like \(-4x^2 - 5 = -5x^2 - 1\)?
5. How can you check if your solution for \(x\) is correct?

**Tip:** Always remember to perform the same operation on both sides of an equation to maintain equality!

Learn how to solve the equation -4x - 5 = -5x - 1 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear equations by isolating variables. Suitable for students in Grades 7-9.

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