Question

What can you do to bring the variables to the same side in the equation 8p−9=46−3p?

You can add 8p to both sides.

Two of these are correct.

You can add 3p to both sides.

You can subtract 8p from both sides.

Answer 1

To bring the variables to the same side in the equation \( 8p - 9 = 46 - 3p \), you can perform the following operations:

1. **Add \( 3p \) to both sides**: This will move the \( -3p \) from the right side to the left side. The equation will become:
\[
8p + 3p - 9 = 46
\]
which simplifies to:
\[
11p - 9 = 46
\]

2. **Add \( 9 \) to both sides then**: This can also be useful after moving the variables to isolate \( p \).

3. **Add \( 8p \) to both sides**: This will move the \( 8p \) from the left side to the right side. The equation will become:
\[
-9 = 46 - 3p - 8p
\]
which simplifies to:
\[
-9 = 46 - 11p
\]

However, it is **not correct to subtract \( 8p \) from both sides** if you wish to bring \( p \) terms to one side.

Thus, the correct actions for bringing variables to the same side are:
- **Add \( 3p \) to both sides**
- **Add \( 8p \) to both sides**

So, the statement "Two of these are correct" is indeed true if it refers to adding \( 3p \) or \( 8p \).