To isolate the variable terms on one side and the constant terms on the other for the equation \(3x - 5 = -2x + 10\), let's rearrange it step by step:
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Start with the original equation: \[ 3x - 5 = -2x + 10 \]
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Add \(2x\) to both sides to get all the \(x\) terms on one side: \[ 3x + 2x - 5 = 10 \] This simplifies to: \[ 5x - 5 = 10 \]
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Now, add \(5\) to both sides to isolate the constant terms: \[ 5x = 15 \]
So, the variable terms isolated on one side and the constant terms on the other can be represented as:
- \(5x = 15\)
- Alternatively, by moving the constant over, we could express it as \(-15 = -5x\) (which is a rearrangement).
Therefore, the two options from your selection that show the variable terms isolated on one side and the constant terms isolated on the other side are:
- \(5x = 15\)
- \(-15 = -5x\)
(Note: While \(x = 5\) is a valid solution to the original equation, it does not represent the isolation of variable and constant terms.)