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!