MODELING TWO STEP INEQUALITIES

To have better understanding on two-step inequalities, we can use the following algebra tiles to model two-step inequalities.

Example 1 : 

Use algebra tiles to model 3x - 4  ≥  5.

Solution : 

Step 1 :

How can we model the left side of the inequality ?

We find 3x - 4 on the left side of the inequality. So we can use three positive variable tiles and four -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 3x - 4  ≥  5 on the mat.

Example 2 : 

Use algebra tiles to model 2x + 1  <  3.

Solution : 

Step 1 :

How can we model the left side of the inequality ?

We find 2x + 1 on the left side of the inequality. So we can use two positive variable tiles and one +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 3 on the right side of the inequality. So we can use three +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 2x + 1  <  3 on the mat.

Example 3 : 

Use algebra tiles to model 4 - 3x > 5.

Solution : 

Step 1 :

How can we model the left side of the inequality ?

We find 4 - 3x on the left side of the inequality. So we can use  four +1-tiles and three negative variable 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 4 - 3x > 5 on the mat.

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