Question

quinda begins to solve the equation -4.5x + 3 = 2 - 8.5x by adding 8.5x to each side of the equation. which next step would result in the variable terms and constant terms being on different sides of the equals sign?

• subtract 4x from both sides.
• subtract 2 from both sides.
• add 4x to both sides.
• subtract 3 from both sides.

Explanation:

Step1: Perform the first step (adding 8.5x)

Start with the equation \(-4.5x + 3 = 2 - 8.5x\). Add \(8.5x\) to both sides:
\(-4.5x + 8.5x + 3 = 2 - 8.5x + 8.5x\)
Simplify: \(4x + 3 = 2\).

Step2: Analyze the goal (separate variable and constant terms)

We need to get the variable term (\(4x\)) and constant terms (\(3\) and \(2\)) on different sides. To do this, we can eliminate the constant term from one side.

Step3: Evaluate each option

• Option 1 (Subtract 4x): \(4x + 3 - 4x = 2 - 4x\) → \(3 = 2 - 4x\) (mixes terms, not desired).
• Option 2 (Subtract 2): \(4x + 3 - 2 = 2 - 2\) → \(4x + 1 = 0\) (mixes terms, not desired).
• Option 3 (Add 4x): \(4x + 3 + 4x = 2 + 4x\) → \(8x + 3 = 2\) (mixes terms, not desired).
• Option 4 (Subtract 3): \(4x + 3 - 3 = 2 - 3\) → \(4x = -1\) (variable term on left, constant on right—success!).

Answer:

D. Subtract 3 from both sides.