MODEL AND SOLVE TWO STEP INEQUALITIES
We will be using the following algebra tiles to model and solve two step inequalities.
Example 1 :
Use algebra tiles to model and solve 3n + 2 ≥ 11.
Solution :
Step 1 :
How can we model the left side of the inequality ?
We find 3n + 2 on the left side of the inequality. So we can use three positive variable tiles and two +1 tiles to model the left side of the inequality.
Step 2 :
How can we model the right side of the inequality ?
We find positive 11 on the right side of the inequality. So we can use eleven +1 tiles to model the right side of the inequality.
Step 3 :
Now use the above mentioned algebra tiles or draw them to model the inequality on the mat.
Step 4 :
Remove two +1 tiles from each side of the mat.
Step 5 :
Divide each side into 3 equal groups.
Step 6 :
The solution is n ≥ 3.
Example 2 :
Use algebra tiles to model 2x - 3 < 5.
Solution :
Step 1 :
How can we model the left side of the inequality ?
We find 2x - 3 on the left side of the inequality. So we can use two positive variable tiles and three -1-tiles to model the left side of the inequality.
Step 2 :
How can we model the right side of the inequality ?
We find positive 5 on the right side of the inequality. So we can use five +1 tiles to model the right side of the inequality.
Step 3 :
Now use the above mentioned algebra tiles or draw them to model the inequality on the mat.
Step 4 :
Add three +1 tiles on each side of the mat.
Step 5 :
Identify and remove zero pairs on each side of the mat.
Step 6 :
Divide each side into 2 equal groups.
Step 7 :
The solution is x < 4.
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