MODELING EQUIVALENT EXPRESSIONS

Two expressions are equivalent, if they are equal in value, when we plug the same value for the variable which exists in the expressions. 

We can use models to determine if two expressions are equivalent. Algebra tiles are one way to model expressions.

Example 1 :

Consider the two expressions 3(x + 2) and 3x + 6 and answer the following questions.  

Question (i)

Model each expression using algebra tiles. 

Answer :

Question (ii)

How many x tiles and 1 tiles does the expression 3(x + 2) have ? 

Answer :

From the above model of 3(x + 2), we have three x tiles and six 1 tiles. 

Question (iii)

How many x tiles and 1 tiles does the expression 3x + 6 have ? 

Answer :

From the above model of 3x + 6, we have three x tiles and six 1 tiles. 

Question (iv)

Is the expression 3(x + 2) equivalent to 3x + 6? Explain.

Answer :

Yes ; each expression is represented by three x tiles and six 1 tiles.

Example 2 :

Consider the two expressions 2(x + 3) and 2x + 3 and answer the following questions.  

Question (i)

Model each expression using algebra tiles. 

Answer :

Question (ii)

How many x tiles and 1 tiles does the expression 2(x + 3) have ? 

Answer :

From the above model of 2(x + 3), we have two x tiles and six 1 tiles. 

Question (iii)

How many x tiles and 1 tiles does the expression 2x + 3 have ? 

Answer :

From the above model of 2x + 3, we have two x tiles and three 1 tiles. 

Question (iv)

Is the expression 2(x + 3) equivalent to 2x + 3 ? Explain.

Answer :

No; 2(x + 3) is represented by two x tiles and six 1 tiles. 2x + 3 is represented by two x tiles and three 1 tiles.

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