Zero Pairs
📚 What You'll Learn
- Setting up equations with parentheses using the distributive property
- Making copies of groups inside parentheses
- Using balanced moves to get cups on one side and cubes on the other
- Proving your answer by substituting back into the original equation
In this example, we are given an equation three parenthesis x plus three equals two x plus sixteen.
Let's start by setting this up using cups and cubes on the problem solving mat.
Begin with the left side of the equation. Remember, we always start by setting up what is shown inside of the parenthesis. X plus three. The three outside of the parenthesis tells us to make three copies of the cups and the cubes.
And now for the right side. Two cups and sixteen cubes.
Now let's use balanced moves to accomplish our goal. To get all of the cups on one side and the cubes on the other.
The left side has fewer cubes, so let's remove all nine of these. And whatever we do to one side, we must do to the other. There goes nine cubes from the right side.
After this balanced move, our mat now shows the equation three x equals two x plus seven.
We have not yet achieved our goal, so let's make a balanced move to remove the two cups from the right side with two cups from the left side.
We now have one cup balanced with seven cubes. X equals seven.
We can prove our answer by inserting seven for x in the original equation. Three times parenthesis seven plus three equals two times seven plus sixteen. Thirty equals thirty. It checks out.
And now you are ready to solve equations that use the distributive property.