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:
- 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:
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–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.
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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.
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–4x = –3: This can be rewritten as \(4x = 3\), which does satisfy the condition of isolating the variable term from the constant.
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3 = 4x: This is already in the desired form, with the variable on one side and the constant on the other.
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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