Select all of the steps that are possible when solving for x.

512x+23x=37
A x = 37
B x = 6
C 37x = 6
D 376x=37
E 112x+23x=37

To solve the equation \( 512x + 23x = 37 \) for \( x \), let's identify which steps are possible:

1. **Combine like terms** on the left side:
   \[
   (512x + 23x) = 535x
   \]
   So, the equation becomes:
   \[
   535x = 37
   \]

2. **Divide both sides by 535** to solve for \( x \):
   \[
   x = \frac{37}{535}
   \]

Given this solution process, let's evaluate the options:

- **A: \( x = 37 \)** - Not possible because \( x \) is not directly equal to 37.
- **B: \( x = 6 \)** - Not possible because \( x \) is not equal to 6.
- **C: \( 37x = 6 \)** - Not possible because this step doesn't appear in the solving process.
- **D: \( 376x = 37 \)** - Not possible, as this doesn't align with the correct steps.
- **E: \( 512x + 23x = 37 \)** - **Possible** because this is the original equation.

The only correct option that reflects a possible step is **E**.

Would you like more details or have any other questions? Here are five related questions for further exploration:

1. How do you combine like terms in an equation?
2. What is the importance of isolating the variable when solving equations?
3. How do you check if your solution to an equation is correct?
4. Can you solve \( 37x = 6 \) and explain why it doesn’t match our scenario?
5. What is the significance of the coefficients in linear equations?

**Tip:** Always double-check each step in solving equations to ensure accuracy.

Explore the step-by-step process to solve the linear equation 512x + 23x = 37. Learn how to combine like terms, isolate the variable, and verify solutions. Suitable for Grades 7-9.

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