Question
What can you do to bring the variables to the same side in the equation 12x+5=2x−15?
Two of these are correct.
You can subtract 12x from both sides.
You can subtract 2x from both sides.
You can add 2x to both sides.
Two of these are correct.
You can subtract 12x from both sides.
You can subtract 2x from both sides.
You can add 2x to both sides.
Answers
GPT-4o mini
To bring the variables to the same side in the equation \(12x + 5 = 2x - 15\), you can use the following methods:
1. **Subtract \(2x\) from both sides**:
\[
12x + 5 - 2x = 2x - 15 - 2x
\]
This simplifies to:
\[
10x + 5 = -15
\]
2. **Subtract \(12x\) from both sides**:
\[
12x + 5 - 12x = 2x - 15 - 12x
\]
This simplifies to:
\[
5 = -10x - 15
\]
Both methods are correct for bringing the variables to the same side.
3. **Add \(2x\) to both sides**:
\[
12x + 5 + 2x = 2x - 15 + 2x
\]
This simplifies to:
\[
14x + 5 = -15
\]
So, from the options given, you can **subtract \(12x\) from both sides** and **subtract \(2x\) from both sides**. Adding \(2x\) to both sides is also a valid operation.
Thus, the correct operations from your options are:
- Subtract \(12x\) from both sides
- Subtract \(2x\) from both sides
However, note that adding \(2x\) is also a valid option but not a direct way to bring all variables to one side since it moves the equation in a slightly different direction.
1. **Subtract \(2x\) from both sides**:
\[
12x + 5 - 2x = 2x - 15 - 2x
\]
This simplifies to:
\[
10x + 5 = -15
\]
2. **Subtract \(12x\) from both sides**:
\[
12x + 5 - 12x = 2x - 15 - 12x
\]
This simplifies to:
\[
5 = -10x - 15
\]
Both methods are correct for bringing the variables to the same side.
3. **Add \(2x\) to both sides**:
\[
12x + 5 + 2x = 2x - 15 + 2x
\]
This simplifies to:
\[
14x + 5 = -15
\]
So, from the options given, you can **subtract \(12x\) from both sides** and **subtract \(2x\) from both sides**. Adding \(2x\) to both sides is also a valid operation.
Thus, the correct operations from your options are:
- Subtract \(12x\) from both sides
- Subtract \(2x\) from both sides
However, note that adding \(2x\) is also a valid option but not a direct way to bring all variables to one side since it moves the equation in a slightly different direction.