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

An easy example of equivalent expressions can be found with the Distributive Property:equivpic
The Distributive Property ensures that 3(x + 2) and 3x + 6 are equivalent expressions.
To double check, we substituted the number 5 into each expression and got the result 21 from both.

You can determine that expressions are equivalent:

• algebraically:
by showing, through algebraic computations, that both expressions can be represented as the same expression.
    - remove parentheses
    - combine similar terms
    - arrange terms from both
           expressions in the same order
    - keep working until both
           expressions are exactly the same		 • numerically:
by showing, through numerical substitution, that the same number(s) replacing the variable(s) in both expressions yield the same numeric results.
    - substitute the same number(s) for each
           variable in each expression
    - compute the numerical results of each            expression
    - the numerical results will be the same           for both expressions
NOTE: Avoid choosing the number 0 for substituting.

When looking for equivalent expressions, you may notice that one of the expressions may appear already expanded and simplified, such as 3x + 6, while the other is in a form that can be expanded and simplied further, such as 3(x + 2). If this is the case, start work on the expression that can be simplified further. If both expressions need further work, it makes no difference where you start.

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hint gal
When determining equivalent expressions,
take your time and LOOK CAREFULLY!
Some expressions may not LOOK equivalent at first glance,
but upon further examination will be equivalent.

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expin1
Are these expressions equivalent?
    7x + 2x and 14x

(Let x = 3)
First expression:
Second expression:
Numerical check:
7(3) + 2(3) = 27
14(3) = 42
27 ≠ 42
 Algebraic check:
 7x + 2x = 9x
14x
9x ≠ 14x
Answer:
NO

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expin2
Are these expressions equivalent?
    18x + 27 and 9(2x + 3)
(Let x = 3)
First expression:
Second expression:
Numerical check
18(3) + 27 = 81
9(2(3)+3) = 81
CHECK		 Algebraic check:
18x +27
 9(2x + 3) = 18x + 27
Distributive Property
CHECK
Answer:
YES
In this example, the Distributive Property shows that expanding the right side, 9(2x + 3),
give us the left side, 18x + 27. You could also have worked the Distributive Property in reverse on the left side.

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expin3
Are these expressions equivalent?
    6(3x) and 9x

(Let x = 3)
First expression:
Second expression:
Numerical check
6(3(3)) = 54
9(3) = 27
54 ≠ 27
 Algebraic check:
6(3x) = 18x
9x
18x ≠  9x
Answer:
NO

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expin4

Which of the following expressions is equivalent to
6x - 5 for all values of x?

1) 3(2x - 5)
3(2x + 5) = 6x + 15 which is not the same as 6x - 5.
2) 3(2x - 1) + 2

 3(2x - 1) + 2 = 6x - 3 + 2 = 6x - 1 which is not the same as 6x - 5.
3) 6(x - 5)

 6(x - 5) = 6x - 30 which is not the same as 6x - 5.
4) 6(x - 1) + 1
ANSWER
 6(x - 1) + 1 = 6x - 6 + 1 = 6x - 5 which is equivalent to 6x - 5.

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expin5
Which of the following expressions is equivalent to
exp?

1) 2(5a +1)
ANSWER

 exp5
2) exp4

 exp6
3) 10a + 1


 4xp7
4) exp8

 exp9


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