Which statements are true when using algebra tiles to solve the equation 8x + (–4) = 11x + 5? Check all that apply.

Question

Add 8 negative x-tiles to both sides of the equation to create a zero pair on the left side.
Add 11 positive x-tiles to both sides of the equation to create a zero pair on the right side.
Add 4 positive unit tiles to both sides of the equation to create a zero pair on the right side.
Add 5 negative unit tiles to both sides of the equation to create a zero pair on the right side.
Divide both groups by 3.
The solution is x = 3.

Answer 1

To solve the equation \(8x + (–4) = 11x + 5\) using algebra tiles, let's analyze the statements given and determine which are true.

1. Add 8 negative x-tiles to both sides of the equation to create a zero pair on the left side.

   • True: Adding 8 negative x-tiles to both sides effectively cancels out the \(8x\) on the left side.

2. Add 11 positive x-tiles to both sides of the equation to create a zero pair on the right side.

   • False: If you add 11 positive x-tiles to both sides, it won't create a zero pair on the right side; instead, it will increase the number of x-tiles on both sides.

3. Add 4 positive unit tiles to both sides of the equation to create a zero pair on the right side.

   • False: Adding 4 positive unit tiles to both sides does not help create a zero pair on the right side because it increases the constant on both sides, thereby moving away from the goal of simplifying the equation.

4. Add 5 negative unit tiles to both sides of the equation to create a zero pair on the right side.

   • True: Adding 5 negative unit tiles to both sides can help eliminate the \(+5\) on the right side, simplifying the equation further.

5. Divide both groups by 3.

   • False: You do not divide both groups by 3 in this context. You typically combine like terms instead of dividing the quantities.

6. The solution is x = 3.

   • True: Once you complete the solution steps correctly, you will arrive at \(x = 3\) as the solution to the equation.

In summary, the true statements are:

• Add 8 negative x-tiles to both sides of the equation to create a zero pair on the left side.
• Add 5 negative unit tiles to both sides of the equation to create a zero pair on the right side.
• The solution is x = 3.