Let's solve the equation step by step:

Given:
\[
3x - (2x - 1) = -9x - 1
\]

### Step 1: Simplify both sides of the equation
Distribute the negative sign on the left-hand side:
\[
3x - 2x + 1 = -9x - 1
\]
This simplifies to:
\[
x + 1 = -9x - 1
\]

### Step 2: Move all terms involving \(x\) to one side and constants to the other side
Add \(9x\) to both sides:
\[
x + 9x + 1 = -1
\]
This simplifies to:
\[
10x + 1 = -1
\]

### Step 3: Isolate \(x\)
Subtract 1 from both sides:
\[
10x = -2
\]

### Step 4: Solve for \(x\)
\[
x = \frac{-2}{10} = \frac{-1}{5}
\]

Thus, the solution is:
\[
x = -\frac{1}{5}
\]

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

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Here are 5 related questions to explore:
1. How do you solve an equation with variables on both sides?
2. What happens when you distribute a negative sign in an equation?
3. How do you check if your solution to an equation is correct?
4. What are the steps to simplify an equation with parentheses?
5. How do you handle equations with fractions?

**Tip**: Always double-check your work by substituting your solution back into the original equation!

Learn how to solve the linear equation 3x − (2x − 1) = −9x − 1 with a detailed, step-by-step guide. This example covers algebraic concepts like simplifying expressions, distributing negative signs, and isolating variables. Suitable for students in Grades 7-9.

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