$$ \frac94 $$$$ \cdot\frac{40}{7} $$$$ \frac{22}{9} $$$$ -x=4 $$

To solve the equation $ \frac{9}{4} \cdot \frac{40}{7} \cdot \frac{22}{9} - x = 4 $, let's follow these steps:

1. Simplify the product of the fractions.
2. Solve for $ x $.

First, let's simplify the product of the fractions:

\[ \frac{9}{4} \cdot \frac{40}{7} \cdot \frac{22}{9} \]

We can start by canceling common factors in the numerator and the denominator:

- The $ 9 $ in the numerator of the first fraction cancels with the $ 9 $ in the denominator of the third fraction.
- This simplifies the expression to:

\[ \frac{40}{4} \cdot \frac{22}{7} \]

Next, simplify $ \frac{40}{4} $:

\[ \frac{40}{4} = 10 \]

So the expression becomes:

\[ 10 \cdot \frac{22}{7} \]

Now, multiply $ 10 $ by $ \frac{22}{7} $:

\[ 10 \cdot \frac{22}{7} = \frac{220}{7} \]

So, the simplified product of the fractions is $ \frac{220}{7} $.

Now we have:

\[ \frac{220}{7} - x = 4 \]

To isolate $ x $, add $ x $ to both sides of the equation and then subtract 4 from both sides:

\[ \frac{220}{7} - 4 = x \]

To simplify $ \frac{220}{7} - 4 $, express 4 as a fraction with a denominator of 7:

\[ 4 = \frac{28}{7} \]

Now subtract $ \frac{28}{7} $ from $ \frac{220}{7} $:

\[ \frac{220}{7} - \frac{28}{7} = \frac{220 - 28}{7} = \frac{192}{7} \]

Therefore,

\[ x = \frac{192}{7} \]

So, the value of $ x $ is $ \frac{192}{7} $.

Do you want details or have any questions? 

Here are 8 related questions that expand on this information:

1. How do you multiply and simplify fractions in general?
2. Can you explain how to convert whole numbers to fractions for subtraction?
3. What are common mistakes to avoid when simplifying fraction multiplications?
4. How do you handle complex fractions in equations?
5. What are the steps to isolate a variable in an algebraic equation?
6. How do you convert improper fractions to mixed numbers?
7. Can you provide an example of solving an equation with multiple fractions and variables?
8. How does fraction cancellation work in simplifying expressions?

**Tip:** Always check if you can simplify fractions before multiplying to make calculations easier.

Learn how to solve the equation $ \frac{9}{4} \cdot \frac{40}{7} \cdot \frac{22}{9} - x = 4 $ step-by-step with a detailed solution. This problem involves fractions, multiplication, and algebraic manipulation. Suitable for high school students.

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