"Expressions" that represent the same value may appear in several different forms,
referred to as equivalent expressions.
When determining equivalent expressions:
take your time and LOOK CAREFULLY!
Some expressions may not LOOK equivalent at first glance,
but upon further examination they will be equivalent.

If you are having trouble determining if expressions are equivalent, plug the same number into each expression
to see if each expression gives the same result.
NOTE: Avoid choosing the numbers 0 and 1 for substituting.

The number 3 will be used for the numerical checks in the following examples.

Are these expressions equivalent?
7x + 2x and 14x

Numerical check
7(3) + 2(3) = 27
14(3) = 42
27
≠ 42 
Algebraic check:
7x + 2x = 9x
9x ≠ 14x 
Not Equivalent!


Are these expressions equivalent?
5(x  2) and 5x  10

Numerical check
5(3  2) = 5
5(3)  10 = 5
CHECK 
Algebraic check:
5(x  2) = 5x  10
Distributive Property
CHECK 
Equivalent!


Are these expressions equivalent?
6(3x) and 9x

Numerical check
6(3(3)) = 54
9(3) = 27
54
≠ 27 
Algebraic check:
6(3x) = 18x
9x
≠ 18x

Not Equivalent!


Which of the following expressions are equivalent to
6(x + 2)? 
The distributive property shows that 6(x + 2) equals 6x + 12. Also, 6(3 + 2) = 6(5) = 30
Expression 
Y/N 
Numerical Check 
Algebraic Check 
a) 6x + 2 
NO 
6(3) + 2 = 20 ≠ 30 
6x + 2 ≠ 6(x + 2) = 6x + 12

b) 3x + 6 + 3x + 6 
YES 
3(3) + 6 + 3(3) + 6 = 30 
3x + 6 + 3x + 6 = 6x + 12

c) 6x + 12 
YES 
6(3) + 12 = 30 
6x + 12 = 6(x + 2) = 6x + 12

d) 3(x + 2) + 3(x + 2) 
YES 
3(3 + 2) + 3(3 + 2) = 30 
3(x + 2) + 3(x + 2) =
3x + 6 + 3x + 6 = 6x + 12

e) 3(x + 2) + 3x 
NO 
3(3 + 2) + 3(3) =
24 ≠ 30 
3(x + 2) + 3x = 3x + 6 + 3x
= 6x + 6 ≠ 6x + 12

The graphing calculator can also be used to evaluate expressions.
Click on the link at the right to see the possibilities. 

For calculator help with Evaluating Expressions
click here. 


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