Let's solve the inequality step by step:

The inequality given is:

$-9 + 4x > 23$

Step 1: Add 9 to both sides of the inequality

$4x > 23 + 9$ $4x > 32$

Step 2: Divide both sides by 4 to solve for $x$

$x > \frac{32}{4}$ $x > 8$

Solution:

The inequality is $x > 8$.

Step 3: Graphing the Solution

• On the number line, plot an open circle at $x = 8$ because the inequality is strictly greater than (no "equal to").
• Shade the region to the right of 8, indicating all values greater than 8.

Inequality Notation:

The inequality is written as $x > 8$.

For the graph:

• Open circle on 8.
• Arrow pointing to the right, covering values greater than 8.

Would you like more details on graphing or other related questions?

Here are 5 follow-up questions to deepen understanding:

1. How would the graph change if the inequality was $x \geq 8$?
2. What would the solution be if the inequality was $-9 + 4x < 23$?
3. Can you explain why we divide both sides by 4 to solve for $x$?
4. How would the result change if the coefficient of $x$ was negative, say $-4x$ instead of $4x$?
5. What are the differences between strict inequalities (like $>$ or $<$) and inclusive inequalities (like $\geq$ or $\leq$)?

Tip: Always pay attention to whether the inequality symbol includes equality (≥, ≤) or not (>, <) when plotting the graph!