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решить с помощью основного свойства пропорции

To solve the given proportion using the cross-multiplication method, which is based on the fundamental property of proportions, we proceed as follows:

### Given Proportion:

\[
\frac{x}{10.5 \cdot 0.24 - 2.02} = \frac{9 \cdot \left(\frac{11}{20} - \frac{0.945}{0.9}\right)}{\frac{3}{40} - \frac{3}{8} \cdot 7}
\]

### Step 1: Cross-Multiply

Using the fundamental property of proportions, cross-multiply to get:

\[
x \cdot \left(\frac{3}{40} - \frac{3}{8} \cdot 7\right) = \left(10.5 \cdot 0.24 - 2.02\right) \cdot 9 \cdot \left(\frac{11}{20} - \frac{0.945}{0.9}\right)
\]

### Step 2: Simplify the left-hand side

First, simplify the expression \( \frac{3}{40} - \frac{3}{8} \cdot 7 \).

Calculate \( \frac{3}{8} \cdot 7 \):

\[
\frac{3}{8} \cdot 7 = \frac{21}{8} = 2.625
\]

Now subtract:

\[
\frac{3}{40} - 2.625 = 0.075 - 2.625 = -2.55
\]

So, the left-hand side becomes:

\[
x \cdot (-2.55)
\]

### Step 3: Simplify the right-hand side

Now, simplify the expression \( 10.5 \cdot 0.24 - 2.02 \):

\[
10.5 \cdot 0.24 = 2.52
\]

Then:

\[
2.52 - 2.02 = 0.5
\]

Next, simplify the expression \( \frac{11}{20} - \frac{0.945}{0.9} \).

Calculate \( \frac{0.945}{0.9} \):

\[
\frac{0.945}{0.9} = 1.05
\]

Then:

\[
\frac{11}{20} - 1.05 = 0.55 - 1.05 = -0.5
\]

Finally, calculate:

\[
9 \cdot (-0.5) = -4.5
\]

So, the right-hand side becomes:

\[
0.5 \cdot (-4.5) = -2.25
\]

### Step 4: Solve for \(x\)

We now have the equation:

\[
x \cdot (-2.55) = -2.25
\]

To solve for \(x\), divide both sides by \(-2.55\):

\[
x = \frac{-2.25}{-2.55} \approx 0.882
\]

### Final Answer:

\[
x \approx 0.882
\]

This is the solution for \(x\) using the fundamental property of proportions.

Would you like to discuss any part of this process in more detail or ask any questions?

### Related Questions:
1. What is the fundamental property of proportions?
2. How can cross-multiplication be used to solve proportions?
3. What are some common errors to avoid in solving proportions?
4. How can you verify your solution in a proportion problem?
5. How do negative numbers affect proportional equations?

### Tip:
When using the cross-multiplication method, always simplify each side as much as possible before performing the multiplication to avoid unnecessary errors.

Learn how to solve a proportion using the cross-multiplication method and the fundamental property of proportions. This detailed guide includes step-by-step calculations and simplifications of expressions involved. Suitable for high school students.

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