To solve the inequality $-2x + 9 < 5$, follow these steps:

Step 1: Isolate the variable

Subtract 9 from both sides of the inequality:

$-2x + 9 - 9 < 5 - 9$

This simplifies to:

$-2x < -4$

Step 2: Solve for $x$

Divide both sides by $-2$. Remember that when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips:

$x > \frac{-4}{-2}$

This simplifies to:

$x > 2$

Step 3: Graph the solution on the number line

• Draw a number line.
• Place an open circle at $x = 2$ to indicate that $2$ is not included in the solution.
• Shade the number line to the right of $x = 2$ to show that $x > 2$.

Step 4: Write the solution in interval notation

The solution in interval notation is:

$(2, \infty)$

This indicates that $x$ can be any number greater than 2.

Would you like to see the graph or need any more details?

---

Here are five related questions you might be interested in:

1. How do you solve a compound inequality?
2. What happens if the inequality is $-2x + 9 \leq 5$?
3. How do you solve absolute value inequalities?
4. What is the difference between a strict inequality and a non-strict inequality?
5. How do you solve a quadratic inequality?

Tip: Always remember to flip the inequality sign when multiplying or dividing by a negative number.