Use the algebra tiles tool to model the equation

Question

5x + (–6) = 6x + 4. What is needed to model the equation? Check all that apply.
5 negative x-tiles on the left
6 positive x-tiles on the right
4positive unit tiles on the right
6 negative x-tiles on the right
6 negative unit tiles on the left

Answer 1

To model the equation \(5x + (–6) = 6x + 4\) using algebra tiles, we need to represent both sides of the equation using tiles that represent the variables (x-tiles) and the constants (unit tiles).

Let's break down the equation:

• On the left side, we have \(5x\) and \(-6\).

  • This can be represented with 5 positive x-tiles (for \(5x\)) and 6 negative unit tiles (for \(-6\)).

• On the right side, we have \(6x\) and \(4\).

  • This can be represented with 6 positive x-tiles (for \(6x\)) and 4 positive unit tiles (for \(4\)).

Now, let's check what is needed to model the equation:

1. 5 negative x-tiles on the left - Not needed (We need positive x-tiles, not negative).
2. 6 positive x-tiles on the right - Needed (This represents \(6x\)).
3. 4 positive unit tiles on the right - Needed (This represents the constant \(4\)).
4. 6 negative x-tiles on the right - Not needed (We need positive x-tiles, not negative).
5. 6 negative unit tiles on the left - Needed (This represents \(-6\), since we require negative unit tiles to model \(-6\)).

In summary, the correct selections for modeling the equation are:

• 6 positive x-tiles on the right
• 4 positive unit tiles on the right
• 6 negative unit tiles on the left