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Equivalent Equations
Justify your reasoning.
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Learning Goal for Focus 2
(HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3):
The student will create equations from multiple representations and solve
linear equations and inequalities in one variable explaining the logic in each
step.
4
3
2
1
0
In addition to
level 3.0 and
above and
beyond what was
taught in
class, the
student may:
- Make
connection with
other concepts
in math
- Make
connection with
other content
areas.
The student will
create equations
from multiple
representations and
solve linear equations
and inequalities in one
variable explaining
the logic in each step.
- rearrange formulas
to highlight a quantity
of interest.
-Graph created
equations on a
coordinate graph.
The student will
be able to solve
linear equations
and inequalities in
one variable and
explain the logic
in each step.
- Use equations
and
inequalities in
one variable to
solve
problems.
With help
from the
teacher,
the student
has
partial
success
with solving
linear
equations
and
inequalities
in one
variable.
Even with
help, the
student
has no
success
with
solving
linear
equations
and
inequalities
in one
variable.
Write an equation that is
true when…
1.
x=0
Examples:
1. 3x = 0
2. t = 1 or -1
2. 5t – 4 = 1
3.
y = -0.5
3. -32y - 24 = -8
4.
z=π
4. z(52) = 25π
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Why would each of the following
equations have the SAME solution set?
(A solution set is the group of all answers to an equation.)
3x = 1 + x and 3x = x + 1
The commutative property.
3x = (1 + x) + 5 and 3x = 1 + (x + 5)
The associative property.
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Would each of the following equations
have the same solution set?
Why or why not?
3x = 1 + x and 3x + 500 = 1 + x + 500
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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Write an equation that would be
equivalent to…
• -6x - 4 = x – 9
• 16x – 8 = 4x
• What algebraic
property did you
use?
• What algebraic
property did you
use?
• Share your equation
with a neighbor to
verify that it is
equivalent.
• Share your equation
with a neighbor to
verify that it is
equivalent.
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The equation 2x + 4 = 6x – 2 is equivalent to all of
the following. Which property was used to
change the equation?
1. -2x – 4 = -6x + 2
1. Multiplication property (•-1)
2. 4 = 4x – 2
2. Subtraction property (-2x)
3. 2x + 2 = 6x – 4
3. Subtraction property (-2)
4. 3x + 4 = 7x – 2
4. Addition property (+x)
5.
5. Division property (÷2)
x + 2 = 3x – 1
6. 2x – 1 = 6x - 7
6. Subtraction property (-5)
Match up equations with the same
solution. Explain how you know they had
the same solution using properties.
A.
B.
C.
D.
E.
F.
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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