The equation \( 3x - 1 = -3 \) is an example of the application of the **Addition Property of Equality** and the **Division Property of Equality** in algebra. Here’s how we can solve this:

### Step-by-step solution:
1. **Start with the equation:**
   \[
   3x - 1 = -3
   \]

2. **Use the Addition Property of Equality** to add 1 to both sides, eliminating the constant on the left-hand side:
   \[
   3x - 1 + 1 = -3 + 1
   \]
   Simplifying:
   \[
   3x = -2
   \]

3. **Use the Division Property of Equality** to divide both sides by 3 to isolate \(x\):
   \[
   \frac{3x}{3} = \frac{-2}{3}
   \]
   Simplifying:
   \[
   x = -\frac{2}{3}
   \]

### Properties used:
1. **Addition Property of Equality:** Adding the same number to both sides of an equation keeps the equation balanced.
2. **Division Property of Equality:** Dividing both sides of the equation by the same non-zero number keeps the equation balanced.

Would you like any more details or have questions about this solution?

Here are 5 related questions:
1. What is the Subtraction Property of Equality?
2. Can the equation \( 3x - 1 = -3 \) be solved using other methods?
3. How would this process differ if there was a multiplication or division on both sides?
4. Can you solve similar equations with variables on both sides of the equation?
5. How can you check if your solution is correct?

**Tip:** Always remember to check your solution by substituting the value of \(x\) back into the original equation!

Learn how to solve the linear equation 3x - 1 = -3 using the Addition and Division Properties of Equality. This step-by-step solution is perfect for students in Grades 6-8 learning foundational algebraic concepts.

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