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To determine the correct transformation for solving the equation \(36 + 6x = 12x - 18\), let's simplify and solve it step by step.

Given equation:
\[ 36 + 6x = 12x - 18 \]

To isolate \(x\), let's perform the following steps:

1. **Subtract \(6x\) from both sides** to get all \(x\) terms on one side:
   \[ 36 + 6x - 6x = 12x - 6x - 18 \]
   \[ 36 = 6x - 18 \]

2. **Add 18 to both sides** to isolate the \(6x\) term:
   \[ 36 + 18 = 6x - 18 + 18 \]
   \[ 54 = 6x \]

3. **Divide both sides by 6** to solve for \(x\):
   \[ \frac{54}{6} = \frac{6x}{6} \]
   \[ 9 = x \]

From the options given:
- Multiplikation mit 3 (Multiplication by 3)
- Subtraktion von 18 (Subtraction by 18)
- Addition von \(6x\) (Addition of \(6x\))
- Division durch 6 (Division by 6)

The most direct and relevant step among the choices provided for solving the equation is **Subtraktion von 18 (Subtraction by 18)**, which aligns with step 2 in the solution process.

Therefore, the correct choice is:
- **Subtraktion von 18 (Subtraction by 18)**

Would you like any further details or have any questions?

Here are 5 relative questions expanding on this information:
1. What are the general steps for solving a linear equation?
2. How can you check if the solution to an equation is correct?
3. What are the properties of equality used in solving equations?
4. Can you provide an example of solving a linear equation with fractions?
5. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always verify your solution by substituting it back into the original equation to ensure it satisfies the equation.

Welche Äquivalenzumformung ist zur Lösung der Gleichung 36 + 6x = 12x − 18 zielführend?

Learn how to solve the linear equation 36 + 6x = 12x − 18 using basic algebraic steps such as subtraction and division. This step-by-step solution helps students in Grades 7-9 understand how to manipulate terms and isolate the variable x.

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