1. Justify your reasoning.
Equivalent Equations
Justify your reasoning.
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2. Write an equation that is true when…
Examples:
3x = 0
5t – 4 = 1
-32y - 24 = -8
z(52) = 25π
x = 0
t = 1 or -1
y = -0.5
z = π
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3. Why would each of the following equations have the SAME solution set?
(A solution set is the group of all answers to an equation.)
5x - 3 = 2(x + 2) and 5x - 3 = 2x + 4
The distributive property.
3x = 1 + x and 3x = x + 1 The commutative property.
12 = (1 + x) + 5 and 12 = 1 + (x + 5) The associative property.
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4. Would each of the following equations have the same solution set
Would each of the following equations have the same solution set? Why or why not?
3x = 1 + x and 3x = 1 + x Yes. The subtraction property of equality could subtract 500 from both sides of the 2nd equation. Then they would be equivalent.
3x = 1 + x and 9x = 3(x + 1) Yes. The division property of equality could divide 3 from both sides of the 2nd equation. Then they would be equivalent.
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5. Write an equation that would be equivalent to…
-6x - 4 = x – 9
What algebraic property did you use?
Share your equation with a neighbor to verify that it is equivalent.
16x – 8 = 4x
What algebraic property did you use?
Share your equation with a neighbor to verify that it is equivalent.
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6. The equation 2x + 4 = 6x – 2 is equivalent to all of the following
The equation 2x + 4 = 6x – 2 is equivalent to all of the following. Which property was used to change the equation?
Multiplication property (•-1)
Subtraction property (-2x)
Subtraction property (-2)
Addition property (+x)
Division property (÷2)
Subtraction property (-5)
-2x – 4 = -6x + 2
4 = 4x – 2
2x + 2 = 6x – 4
3x + 4 = 7x – 2
x + 2 = 3x – 1
2x – 1 = 6x - 7

7. Match up equations with the same solution
Match up equations with the same solution. Explain how you know they had the same solution using properties.
2x – 3 = 5x + 7
2x + 3 = 5x – 7
10x – 8 = 6x + 10
2x – 2 = 5x – 12
4x – 6 = 10x + 14
5x – 4 = 3x + 5
A & E = Multiplication property (•2)
B & D = Subtraction property (-5)
C & F = Division property (÷2)
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