"Expressions" that represent the same value may appear in several different forms,
referred to as equivalent expressions.
equivPic

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.

hint gal
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. 

expin1
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!
frown

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expin2
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!
smile

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expin3
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!
frown

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expin4 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

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The graphing calculator can also be used to evaluate expressions.
Click on the link at the right to see the possibilities.
ti84c
For calculator help with Evaluating Expressions
click here.

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