The image shows the following compound inequality problem:

$3x - 1 < 14 \quad \text{and} \quad 4x + 5 > 11$

Let's solve each part of the compound inequality separately:

1. Solve $3x - 1 < 14$:

$3x - 1 < 14$ Add 1 to both sides: $3x < 15$ Divide both sides by 3: $x < 5$

2. Solve $4x + 5 > 11$:

$4x + 5 > 11$ Subtract 5 from both sides: $4x > 6$ Divide both sides by 4: $x > \frac{6}{4} = 1.5$

3. Combine the results:

The compound inequality requires both conditions to be satisfied simultaneously. Thus, the solution is: $1.5 < x < 5$

This is the final solution, which can be graphed on the number line as an open interval from $1.5$ to $5$.

Do you need help graphing this, or would you like further details on any step?

Here are five related questions to further your understanding:

1. How would the solution change if the inequalities included "≤" or "≥" instead of "<" or ">"?
2. How do you solve a compound inequality if the word "or" is used instead of "and"?
3. Can compound inequalities have no solution? If so, when does that occur?
4. How would you graph $1.5 < x < 5$ on a number line?
5. What happens if you multiply or divide an inequality by a negative number?

Tip: When solving inequalities, always remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign!