Jenny is solving the equation 3 x + 5 = 4 x + 2 using algebra tiles. She cannot decide if she should add 3 negative x-tiles or add 2 negative unit tiles to both sides first. Which explains which Jenny should do first?

Question

She should add 3 negative x-tiles first because that is the only way to isolate the variable.
She should add 2 negative unit tiles first because that is the only way to get to the correct solution.
She can do either one first because zero pairs will be created to isolate the variable either way.
She should do neither one first because the first step is to add 4 negative tiles to both sides.

Answer 1

The correct option is: She can do either one first because zero pairs will be created to isolate the variable either way.

Here's the reasoning: Jenny can choose to either eliminate the x-tiles first or the unit tiles (constants) first.

1. If Jenny adds 3 negative x-tiles to both sides, she would get: \[ 3x - 3x + 5 = 4x - 3x + 2 \implies 5 = x + 2 \]

   Then she would solve for \(x\).

2. If she adds 2 negative unit tiles to both sides, she would have: \[ 3x + 5 - 2 = 4x + 2 - 2 \implies 3x + 3 = 4x \]

   Again, she could solve for \(x\) afterwards.

In both cases, she will be isolating the variable correctly. Each method will lead to the same final result, demonstrating the flexibility in choosing the order of operations when solving the equation using algebra tiles.