4x-4<8 \quad \maroonC{\text{ AND}} \quad 9x+5>23

Let's solve the two inequalities step by step:

### First inequality:  
\[
4x - 4 < 8
\]

1. Add 4 to both sides:
\[
4x < 8 + 4
\]
\[
4x < 12
\]

2. Divide by 4:
\[
x < \frac{12}{4}
\]
\[
x < 3
\]

### Second inequality:  
\[
9x + 5 > 23
\]

1. Subtract 5 from both sides:
\[
9x > 23 - 5
\]
\[
9x > 18
\]

2. Divide by 9:
\[
x > \frac{18}{9}
\]
\[
x > 2
\]

### Combining the two inequalities:
We have:
\[
x < 3 \quad \text{AND} \quad x > 2
\]

Thus, the solution is:
\[
2 < x < 3
\]

Would you like more details on this? 

Here are 5 related questions for further exploration:
1. How would the solution change if we had \( 4x - 4 \leq 8 \) and \( 9x + 5 \geq 23 \)?
2. Can you represent the solution \( 2 < x < 3 \) on a number line?
3. How do the rules for solving inequalities differ from solving equations?
4. What would happen if one inequality had no solution?
5. Can inequalities be solved using graphing techniques?

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

This page offers a step-by-step solution to the compound inequalities 4x - 4 < 8 and 9x + 5 > 23. Understand key concepts of algebra and inequalities as you solve for x. Suitable for students in Grades 7-9.

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