Question

Which equations have the variable term in the equation –6 + 2x = 6x – 9 isolated to one side of the equals sign, and the constant isolated to the other side? Select all that apply.
–6 = 4x – 9
3 – 4x= 0
–4x = –3
3 = 4x
2x= 6x - 3

Answer 1

To find the equations that have the variable term isolated on one side and the constant on the other, we first need to isolate \(2x\) from the original equation:

Starting with the original equation:

\[
-6 + 2x = 6x - 9
\]

Rearranging it to isolate the variable on one side and the constant on the other yields:

1. Move all terms with \(x\) to one side:
\[
-6 + 2x = 6x - 9 \implies -6 + 9 = 6x - 2x
\]

This simplifies to:

\[
3 = 4x
\]

Now, we'll evaluate the given options:

1. **–6 = 4x – 9**: We can rearrange this to isolate the variable and constant, yielding \(4x = 3\), which is not in the form we want since the constant is not isolated on the left side.

2. **3 – 4x= 0**: This can be rearranged to \(3 = 4x\), which matches our desired form of having \(4x\) on one side and \(3\) on the other.

3. **–4x = –3**: This can be rewritten as \(4x = 3\), which does satisfy the condition of isolating the variable term from the constant.

4. **3 = 4x**: This is already in the desired form, with the variable on one side and the constant on the other.

5. **2x= 6x - 3**: Rearranging gives us \(6x - 2x = 3\), or equivalently \(4x = 3\), satisfying our requirement as well.

From the evaluations above, the equations that have the variable term isolated on one side and the constant on the other side are:

- **3 – 4x = 0**
- **–4x = –3**
- **3 = 4x**
- **2x = 6x - 3**

So the selected equations are:

- 3 – 4x = 0
- –4x = –3
- 3 = 4x
- 2x = 6x - 3