https://file.aiquickdraw.com/mathbot/file/1729956413600f2jzg8mu.jpg

The image contains a series of inequalities in Indonesian that ask for solutions for each inequality. Here is the transcription of the inequalities:

### Instructions (in Indonesian):
"Tentukan himpunan penyelesaian pertidaksamaan" — which translates to "Determine the solution set of the inequality."

### Inequalities:
1. \(4x - 7 < 3x + 5\)
2. \(3 \leq 5x + 1 \leq 16\)
3. \(6 \leq x^2 + x < 20\)
4. \(\frac{x + 5}{2x - 1} \leq 0\)
5. \(\frac{6}{x} - 5 + x \leq 0\)
6. \(\frac{7}{x} < \frac{3}{x - 4}\)
7. \(\frac{1}{x + 1} \geq \frac{2}{x - 2}\)
8. \( |x + 1| + 1 < 4\)
9. \( |x - 2| < 3 |x + 7|\)
10. \( \left|\frac{3 - 2x}{1 + x}\right| \leq 4\)

Would you like me to solve each inequality and provide the solution sets? 

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### Further Questions for Exploration:
1. What are the methods used to solve absolute inequalities like those in questions 8-10?
2. How do we interpret compound inequalities like in question 2?
3. What are the steps for solving inequalities involving rational expressions as seen in questions 4 and 5?
4. How can we check if our solution set is correct for inequalities involving absolute values?
5. What are the implications of having variables in the denominator, such as in questions 4, 5, 6, and 7?

**Tip:** When solving inequalities, always pay attention to cases where division or multiplication by a negative number may reverse the inequality sign.

Tentukan himpunan penyelesaian pertidaksamaan

Explore how to determine the solution sets for various types of inequalities, including absolute and rational expressions. This comprehensive solution covers linear, quadratic, absolute value, and rational inequalities, making it ideal for high school students.

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