Question

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

True:
- Add 8 negative x-tiles to both sides to create a zero pair on the left side. (This is equivalent to subtracting 8x from both sides: 8x - 4 → -4, 11x + 5 → 3x + 5.)
- Add 5 negative unit tiles to both sides to create a zero pair on the right side. (This cancels the +5 on the right.)
- Divide both groups by 3. (After the previous steps you get 3x = -9, so divide by 3 to find x.)

False:
- Add 11 positive x-tiles to both sides to create a zero pair on the right side. (You would need negative x-tiles to cancel the 11x on the right.)
- Add 4 positive unit tiles to both sides to create a zero pair on the right side. (Adding +4 cancels the -4 on the left, not anything on the right.)
- The solution is x = 3. (The correct solution is x = -3.)