Question

Emory used these steps to solve the equation.

x + 7 = 3x + (−5).

1. Add 1 negative x-tile to both sides and create zero pairs.

2. Add 7 negative unit tiles to both sides and create zero pairs.

3. Divide the 12 negative unit tiles evenly among the 2 x-tiles.

4. The solution is x = −6.

Where did Emory make an error?
In step 1, he should have added 3 negative x-tiles to both sides.
In step 2, he should have added 5 positive unit tiles to both sides.
In step 3, he did not divide the tiles evenly.
In step 4, he should have found the solution x = 3.

Answer 1

Error in step 3.

After step 2 the model represents 0 = 2x − 12. Emory divided the −12 units among the 2 x-tiles and got x = −6. Instead you must solve 2x − 12 = 0, so 2x = 12 and x = 6. (Equivalently, add 12 positive unit tiles to both sides to cancel the −12, then divide the 12 units among the 2 x-tiles to get x = 6.)