Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options.

Question

x = 5
–15 = –5x
5x = 15
–15 = 5x
x = -5

Answer 1

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:

1. Start with the original equation: \[ 3x - 5 = -2x + 10 \]

2. Add \(2x\) to both sides to get all the \(x\) terms on one side: \[ 3x + 2x - 5 = 10 \] This simplifies to: \[ 5x - 5 = 10 \]

3. 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:

1. \(5x = 15\)
2. \(-15 = -5x\)

(Note: While \(x = 5\) is a valid solution to the original equation, it does not represent the isolation of variable and constant terms.)