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The given equation is:

\[
\sqrt{\frac{2x + 4}{9}} - 0.3 = \sqrt{3} \cdot \sqrt{\frac{3}{9}} - 1.9
\]

Let's simplify and solve this equation step-by-step:

### Step 1: Simplify the Right Side
The right side of the equation is:

\[
\sqrt{3} \cdot \sqrt{\frac{3}{9}} - 1.9
\]

First, simplify the square root multiplication:

\[
\sqrt{3} \cdot \sqrt{\frac{3}{9}} = \sqrt{\frac{3 \times 3}{9}} = \sqrt{\frac{9}{9}} = \sqrt{1} = 1
\]

So, the right side becomes:

\[
1 - 1.9 = -0.9
\]

### Step 2: Rewrite the Equation
Now, substitute the simplified right side back into the original equation:

\[
\sqrt{\frac{2x + 4}{9}} - 0.3 = -0.9
\]

### Step 3: Isolate the Square Root Term
Add \(0.3\) to both sides:

\[
\sqrt{\frac{2x + 4}{9}} = -0.9 + 0.3
\]

\[
\sqrt{\frac{2x + 4}{9}} = -0.6
\]

### Step 4: Analyze the Result
Since the square root of any real number cannot be negative, there is **no real solution** to this equation.

If you have any questions or want more details about specific steps, let me know!

### Related Questions:
1. How do you solve quadratic equations using square roots?
2. What are the properties of square roots when it comes to negative numbers?
3. How can we check if an equation has no real solutions?
4. How do you simplify expressions involving square roots and fractions?
5. What are some methods for solving equations with square roots on both sides?

### Tip:
Always check if a mathematical equation has a possible solution set before proceeding with solving it!

Solve the equation: \(\sqrt{\frac{2x + 4}{9}} - 0.3 = \sqrt{3} \cdot \sqrt{\frac{3}{9}} - 1.9\).

Understand how to solve an equation involving square roots: \(\sqrt{\frac{2x + 4}{9}} - 0.3 = \sqrt{3} \cdot \sqrt{\frac{3}{9}} - 1.9\). Learn key algebraic concepts, including square root properties and simplification rules. This problem is suitable for students in Grades 9-11.

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