Hands-on Algebra: Solving Multi-Step Equations

Just as we used cups and counters to solve one-step equations, they can also be used to solve equations with a variable on each side.
For the demonstration problem, 2x + 2 = -4, place 2 cups and two positive counters on one side of the mat. Place 4 negative counters on the other side of the mat. Notice it is not possible to remove the same kind of counters from each side. 
Add 2 negative counters to each side.
Group the counters to form zero-pairs and remove all zero-pairs. Separate the remaining counters into 2 equal groups to correspond to the 2 cups.
Each cup is matched with 3 negative counters. Therefore, x = -3.

Next, demonstrate solving w - 3 = 2w -1 with a cup and counters. Place 1 cup and 3 negative counters on one side of the mat. Place 2 cups and 1 negative counter on the other side of the mat. 

Remove 1 negative counter from each side of the mat.

Just as you can remove the same kind of counter from each side of the mat, you can remove cups from each side of the mat. In this case, you can remove 1 cup from each side.

The cup on the right, or the unknown, is matched with 2 negative counters. Therefore, the answer to the equation is w= -2.

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