Select all the steps that are possible when solving x

Question

512x+23x=37

1. x = 37
2. x = 6
3. 37x = 6
4. 376x=37
5. 112x+23x=37

Answer 1

To begin solving the equation \( 512x + 23x = 37 \), we can simplify it as follows:

1. Combine like terms on the left side: \[ (512 + 23)x = 37 \] This simplifies to: \[ 535x = 37 \]

2. To find \( x \), divide both sides by 535: \[ x = \frac{37}{535} \]

Now, we can analyze the steps given:

1. \( x = 37 \): Incorrect, as we found \( x = \frac{37}{535} \).
2. \( x = 6 \): Incorrect, as we found \( x = \frac{37}{535} \).
3. \( 37x = 6 \): This step is not directly correct based on the original equation.
4. \( 376x = 37 \): This is incorrect; we had \( 535x = 37 \).
5. \( 112x + 23x = 37 \): This is not correct based on the original equation.

Based on this analysis, the only correct simplification leading from the original equation is: \[ 535x = 37 \]

None of the proposed steps accurately reflect valid operations or solutions derived from the initial equation.