To isolate the variable terms on one side and the constant terms on the other side for the equation \(3x - 5 = -2x + 10\), we can follow these steps:
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Add \(2x\) to both sides to get all \(x\) terms on the left side: \[ 3x + 2x - 5 = 10 \] which simplifies to: \[ 5x - 5 = 10 \]
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Add \(5\) to both sides to get all constant terms on the right side: \[ 5x = 10 + 5 \] which simplifies to: \[ 5x = 15 \]
Putting both transformations together, we can express the original equation as:
- \(5x - 5 = 10\)
- \(5x = 15\)
Thus, the two equations that show the variable terms isolated on one side and the constant terms isolated on the other side are:
- \(5x - 5 = 10\)
- \(5x = 15\)
These two options correctly isolate variable and constant terms on opposite sides.