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The problem in the image reads:

**3. Express in the form of \( ax + by + c = 0 \):**

\[
\sqrt{2}x = 3\sqrt{2}y + 2
\]

### Solution:

We need to rearrange this equation into the form \( ax + by + c = 0 \), where \( a \), \( b \), and \( c \) are constants.

Start with the given equation:

\[
\sqrt{2}x = 3\sqrt{2}y + 2
\]

### Step 1: Move all terms to one side of the equation.

Subtract \( 3\sqrt{2}y \) and \( 2 \) from both sides:

\[
\sqrt{2}x - 3\sqrt{2}y - 2 = 0
\]

### Step 2: The equation is now in the form \( ax + by + c = 0 \), where:
- \( a = \sqrt{2} \),
- \( b = -3\sqrt{2} \),
- \( c = -2 \).

Thus, the equation in the form \( ax + by + c = 0 \) is:

\[
\sqrt{2}x - 3\sqrt{2}y - 2 = 0
\]

Would you like more details on any specific step or have further questions?

Here are some related questions to explore:

1. How would the equation change if we squared both sides?
2. What would happen if we isolated \( y \) instead of \( x \)?
3. Can we simplify the equation further by factoring out \( \sqrt{2} \)?
4. What is the geometric interpretation of this linear equation?
5. How would the coefficients change if we multiplied through by \( \sqrt{2} \)?

**Tip**: Always aim to simplify equations by factoring out common terms when possible.

Express in the form of ax + by + c = 0: sqrt(2)x = 3sqrt(2)y + 2

Learn how to express a linear equation in the form ax + by + c = 0. This problem involves algebraic manipulation and is suitable for students in Grades 10-12.

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