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I see you've uploaded an image of some mathematical inequalities written in French. Here’s a breakdown of the inequalities based on the part visible:

The instruction says: "**Résoudre les inéquations suivantes :**" (which means "Solve the following inequalities:").

The inequalities are as follows:

1. \( \frac{3x}{x - 2} \leq 0 \)
2. \( \frac{3x^2}{2x + 3} > 5 \)
3. \( \frac{2x + 3}{x} \geq 3 \)
4. \( \sqrt{1 + x} \leq 1 - x \)

Would you like me to solve each of these inequalities step by step? Let me know if you have any questions or need a detailed explanation.

Here are 5 questions to further your understanding:

1. What are the steps to solve rational inequalities like the ones presented?
2. How do you handle inequalities that involve square roots and other non-linear terms?
3. Can you describe the difference in approach between solving equations and inequalities?
4. What precautions should be taken when multiplying or dividing inequalities by negative numbers?
5. How can inequalities be represented graphically on a number line?

**Tip:** Always check the domain of the expression, especially when dealing with square roots or rational functions, as these can impose additional restrictions on the solution set.

Solve the inequalities: 1) (3x)/(x-2) ≤ 0, 2) (3x²)/(2x+3) > 5, 3) (2x + 3)/x ≥ 3, 4) √(1 + x) ≤ 1 - x

This page walks through solving a set of rational and nonlinear inequalities, including those with square roots and fractional expressions. Ideal for students in Grades 10-12, the guide explores inequality properties, sign analysis, and handling domain restrictions.

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