https://file.aiquickdraw.com/mathbot/file/17268856551637fawa13p.jpg

Let’s solve the two inequalities shown in the image step by step.

### Question 14: 
Solve the compound inequality:

\[
-15 < 5x - 1 \leq 5
\]

1. Solve the left inequality: \(-15 < 5x - 1\)
   - Add 1 to both sides:  
     \[-15 + 1 < 5x\]  
     \[-14 < 5x\]
   - Divide by 5:  
     \[\frac{-14}{5} < x\]  
     \[x > -\frac{14}{5}\]

2. Solve the right inequality: \(5x - 1 \leq 5\)
   - Add 1 to both sides:  
     \(5x \leq 6\)
   - Divide by 5:  
     \(x \leq \frac{6}{5}\)

The solution as a compound inequality is:

\[
-\frac{14}{5} < x \leq \frac{6}{5}
\]

### Question 15:
Solve the inequality:

\[
-\frac{1}{4}x - 4 < -7
\]

1. Add 4 to both sides:
   \[-\frac{1}{4}x < -3\]
   
2. Multiply both sides by \(-4\) (since multiplying or dividing by a negative number reverses the inequality):
   \[x > 12\]

The solution is:
\[
x > 12
\]

Would you like more detailed explanations for any of these steps? Here are some related questions for further practice:

1. How do you solve compound inequalities in general?
2. What happens when you multiply or divide an inequality by a negative number?
3. How do you express solutions to inequalities on a number line?
4. How can compound inequalities be expressed in interval notation?
5. How do you check if a value satisfies a given compound inequality?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Solve the inequalities: -15 < 5x - 1 ≤ 5 and -1/4x - 4 < -7.

Learn how to solve compound inequalities such as -15 < 5x - 1 ≤ 5 and linear inequalities like -1/4x - 4 < -7. This guide provides a step-by-step explanation of solving inequalities, including handling negative coefficients and reversing inequality signs.

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