https://r2.erweima.ai/mathbot/image/1726186714893gmyco7vu.jpg

In this image, the content on the whiteboard consists of a series of mathematical exercises in Spanish. Let me guide you through the different steps and solve the problems:

### Problem 1: "Hallar el valor de X"
This section consists of two sub-problems where we are asked to find the value of \( X \).

#### 1a) 
\[
-2 \cdot \left( X - \frac{3}{2} \right) = 0.3 \cdot (3.9 - 5X) - \frac{9}{5}
\]
This is an equation involving \( X \), and we will solve it step-by-step.

#### 1b) 
\[
\frac{1}{3} X^3 \cdot \left( 0.4 - 2 \cdot 0.6^2 \right) = \left( \frac{3}{6} \right)^{-2}
\]
This involves simplifying expressions with exponents and solving for \( X \).

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### Problem 2: "Encontrar el valor de los medios o extremos en las proporciones"
Here we are solving proportionality equations, asking for the values of \( X \).

#### 2a) 
\[
\frac{2X - 1}{2} = 5 \cdot \left( \frac{-2}{3} \right)^0
\]
Solve for \( X \).

#### 2b) 
\[
\frac{1 - \frac{16}{25}}{1 - \frac{2}{3}} = \frac{1}{10} + \frac{1}{2} \cdot \frac{1}{X}
\]
We solve this by simplifying both sides and isolating \( X \).

#### 2c) 
\[
\frac{9.3 X}{\sqrt{1 - \frac{4}{9}} \cdot 2} = \frac{1}{10} \cdot \frac{X^{-1}}{3}
\]
This is a proportional equation that involves simplifying square roots and powers of \( X \).

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Would you like me to solve a specific problem from this list, or should I start with one and go through them all? Let me know if you need detailed steps for any of the problems.

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**Relative Questions:**
1. How do you simplify expressions involving both exponents and roots?
2. What are the typical steps to solve equations with variables on both sides?
3. How do proportionality equations differ from regular linear equations?
4. Can you explain the significance of fractions in algebraic equations?
5. What strategies can be applied when simplifying nested fractions?

**Tip:** When working with exponents, always check if simplifying powers early can make the equation easier to handle.

Hallar el valor de X y encontrar el valor de los medios o extremos en las proporciones.

Solve algebraic equations and find values of X in proportionality problems. This covers algebraic simplifications, exponents, and proportion solving methods for students in Grades 9-10.

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