equivalent equations
TRANSCRIPT
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EquationsIts all about equivalence
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An equation ….
Is a mathematical sentence that says that two expressions are equal.
What is on the left = what is on the right
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There are two types of equations …..
Numerical5 + 9 = 14
Algebraic2x – 3 = 14
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Modeling of equations
2x + 4 = -6
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Model these in your notes:
-3x + 4 = 2x
5+ 2x = -1
6x – 3 = -2x + 4
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Our goal with equations is to:
• Find the value of “x” or the variable
• Solve it
To do this we must rewrite the equation in progressively simpler equivalent forms of the original
equation.
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So to do this we need to use the most important rule for
equations …..
What you do to one side you MUST do to the other
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2x + 4 = -6
From the equation we can choose to try the following:
+ 2x -2x
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2x + 4 = -6
From the equation we can choose to try the following:
+ 2x -2x + 4 -4
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2x + 4 = -6
From the equation we can choose to try the following:
+ 2x -2x + 4 -4 -6 + 6
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2x + 4 = -6
From the equation we can choose to try the following:
+ 2x -2x + 4 -4 -6 + 6
x 2 or ÷2
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2x + 4 = -6
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+ 2x to both sides
4x + 4 = 2x - 6
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- 2x on both sides
4=-2x-6
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+ 4 on both sides
2x + 8 = -2
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-4 on both sides
2x = -10
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-6 on both sides
2X – 2 = -12
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+6 on both sides
2x + 10 = 0
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Multiply both sides by 2
4x + 8 = -12
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Divide both sides by 2
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Divide both sides by 2
x + 2 = -3
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None of these steps are WRONG … an equivalent equation results every time
BUTthe ONE operation that makes the
equation simpler (shorter) is the one you are looking for!
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For these, list all the possible things you could do to each side
-3x + 4 = x
5+ 2x = -1
5x – 3 = -2x + 4
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-3x + 4 = x
-3x + 3x
+ 4 -4
+x -x
x -3 ÷ -3
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5+ 2x = -1
+ 5 -5
+ 2x -2x
-1 +1
x 2 ÷ 2
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5x – 3 = -2x + 4
+ 5x -5x
-3 +3
-2x +2x
+ 4 -4
x 5 ÷ 5
x -2 ÷ -2
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For the each of the 3 equations:
- Write out the equivalent form for each
2x + 4 = -6 Possible Resulting equivalent equation
Model of original +2x 4x + 4 = 2x - 6
-2x 4 = -2x - 6
+4 2x + 8 = -2
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