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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