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The inequality you provided is:

\[
-5 - 7x > -9x + 5
\]

Let's solve this step by step.

### Step 1: Move all terms involving \( x \) to one side.
We can add \( 9x \) to both sides to start isolating \( x \):

\[
-5 - 7x + 9x > 5
\]

Simplify:

\[
-5 + 2x > 5
\]

### Step 2: Move the constant terms to the other side.
Now, add 5 to both sides to move the constant to the right-hand side:

\[
2x > 10
\]

### Step 3: Solve for \( x \).
Divide both sides by 2:

\[
x > 5
\]

### Final Answer:
The solution to the inequality is:

\[
x > 5
\]

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

Here are 5 related questions for you:
1. How would the inequality change if it were \( -5 - 7x \geq -9x + 5 \)?
2. What happens if you switch the inequality direction? What does \( x < 5 \) mean in this context?
3. Can you graph the solution \( x > 5 \) on a number line?
4. How would the steps change if there were no \( x \) terms on one side of the inequality?
5. Can you solve an inequality like this if the variable \( x \) appears in both the numerator and denominator?

**Tip:** Always reverse the inequality sign when you multiply or divide both sides by a negative number!

Learn how to solve the linear inequality -5 - 7x > -9x + 5 with a step-by-step solution. This problem explores algebraic concepts and inequalities. Suitable for students in Grades 7-9.

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