Question

Juanita wants to model the equation 3 x + 2 = negative x + 6. She begins with the tiles below. pick one answer

3 x tiles and 2 positive 1 tiles = 1 negative x tile

How can Juanita complete her model?
Put 4 yellow unit tiles on the left side of the equal sign.
Put 4 yellow unit tiles on the right side of the equal sign.
Put 6 green x-tiles on the right side of the equal sign.
Put 6 yellow unit tiles on the right side of the equal sign.

Answer 1

To complete her model for the equation \(3x + 2 = -x + 6\), Juanita starts with \(3x\) tiles and \(2\) positive unit tiles on the left, and \(1\) negative \(x\) tile on the right.

To balance the equation, she needs to isolate the \(x\) terms and the constant terms.

The equation can be rearranged as follows:

1. Add \(x\) to both sides to eliminate the negative \(x\) from the right:
\[
3x + x + 2 = 6
\]
This results in:
\[
4x + 2 = 6
\]

2. Next, subtract \(2\) from both sides to isolate the \(x\) terms:
\[
4x = 4
\]

So, on the right side, to have \(6\) we initially have \(2\) already on the left, which makes three \(2\)s more required on the right to make \(6\).

Thus, she needs to **put 4 yellow unit tiles on the right side of the equal sign.**

So the answer is **Put 4 yellow unit tiles on the right side of the equal sign.**