We can solve the equation \( 3x - 7 = -2x - 9 \) by following these steps:

### Step 1: Move all terms involving \( x \) to one side of the equation.
Add \( 2x \) to both sides:
\[
3x + 2x - 7 = -9
\]
This simplifies to:
\[
5x - 7 = -9
\]

### Step 2: Move the constant term to the other side.
Add 7 to both sides:
\[
5x = -9 + 7
\]
This simplifies to:
\[
5x = -2
\]

### Step 3: Solve for \( x \).
Divide both sides by 5:
\[
x = \frac{-2}{5}
\]

Thus, the solution is:
\[
x = -\frac{2}{5}
\]

Would you like any additional details or explanations?

Here are 5 related questions to extend your understanding:
1. How would you solve the equation \( 4x - 5 = 2x + 3 \)?
2. What happens if you solve the equation \( 3x - 7 = 3x - 9 \)?
3. Can you try solving \( 6x - 4 = -2x + 8 \) by yourself?
4. How would the steps change if the equation was \( 3x - 7 = 2x - 9 \)?
5. What is the next step if you have \( 5x = -15 \) instead?

**Tip**: Always check your solution by substituting it back into the original equation!

Learn how to solve the linear equation 3x - 7 = -2x - 9 with a detailed step-by-step solution. This problem explores essential algebra concepts like moving terms and solving for x. Suitable for students in Grades 6-8.

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