Let's solve the equation:

\[
-2(-5x - 1) + 5x - 3 = -31
\]

### Step 1: Distribute the \(-2\) across \((-5x - 1)\):

\[
-2(-5x) - 2(-1) = 10x + 2
\]

So the equation becomes:

\[
10x + 2 + 5x - 3 = -31
\]

### Step 2: Combine like terms on the left side:

\[
(10x + 5x) + (2 - 3) = 15x - 1
\]

Now the equation is:

\[
15x - 1 = -31
\]

### Step 3: Isolate the variable \(x\):

Add 1 to both sides:

\[
15x = -31 + 1
\]

\[
15x = -30
\]

### Step 4: Solve for \(x\):

\[
x = \frac{-30}{15} = -2
\]

### Final Answer:
\[
x = -2
\]

Would you like more details or have any questions? Here are 5 related questions you might explore:

1. What are the common errors to avoid when distributing a negative sign?
2. How does changing the order of operations affect the solution to an equation?
3. Can you solve an equation by factoring instead of distribution?
4. What strategies can be used to solve multi-step equations efficiently?
5. How do you interpret the solution of a linear equation graphically?

**Tip:** When dealing with negative signs, be careful to correctly distribute them to all terms inside the parentheses.

Learn how to solve the equation -2(-5x - 1) + 5x - 3 = -31 step-by-step with detailed explanations. This problem covers equations, distributive property, and combining like terms. Suitable for students in Grades 7-9.

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