Equivalent Equations
Presentation
•
Mathematics
•
9th Grade
•
Practice Problem
•
Hard
Standards-aligned
Christopher Gassler
Used 23+ times
FREE Resource
11 Slides • 9 Questions
1
Equivalent Equations
Objective: create and identify equivalent equations.
2
Vocabulary
Equivalent: to two meanings, numbers, or quantities that are the same.
Examples:
NOTE: look at each side of the equal sign like it's own seperate entity. NOT like a sentence
3
Example 1: Are the following expressions equivalent?
4 + 2 x 3 - 2 = 44 ÷ 2
2(x + 9) = 24 + 2x - 15
?
?
4
Multiple Select
Choose all the equivalent expressions.
12+12−3x=3(x+8)
8−3×3+5=10−12÷2
4x+12=4x+6+6
56÷7=4+3
5
Open Ended
Are these equivalent? 4x+12=4x+6+6 ...YES
Are they still equaivalent? 4x+12+3=4x+6+6+3 ...YES
Why?
6
ADDITION PROPERTY OF EQUALITY
Adding the same number to both sides of an equal sign makes an equivalent equation.
8 + 5 = 13
is equivalent to
8 + 5 + 4 = 13 + 4
7
SUBTRACTION PROPERTY OF EQUALITY
Subtracting the same number from both sides of an equal sign makes an equivalent equation.
8 + 5 = 13
is equivalent to
8 + 5 - 4 = 13 - 4
8
EXAMPLE
If 5 is added to both sides what is the result?
3x - 15 = 32
9
Fill in the Blanks
Type answer...
10
Fill in the Blanks
Type answer...
11
DIVISION PROPERTY OF EQUALITY
Dividing both sides of an equal sign by the same number makes an equivalent equation.
is equivalent to
10 + 6 = 16
and equivalent to
12
EXAMPLE
If you divide both sides by 3 what is the result?
3x - 15 = 30
13
Fill in the Blanks
Type answer...
14
EXAMPLE
Which equations are equivalent to: 16 - 4x = 36
8 - 2x = 18
12 - x = 32
4 - x = 9
15
Multiple Select
Which equation(s) are equivalent to 7x - 14 = 21 ?
x - 2 = 3
7x - 20 = 15
7x - 14 = 21
16
Multiple Select
Which equations are equivalent to p−h=24 ?
2p−h=12
3p−h=6
−4p−h=−6
−1p−h=23
17
MULTIPLICATION PROPERTY OF EQUALITY
Multiplying both sides of an equal sign by the same number makes an equivalent equation.
is equivalent to
2x - 9 = 3
and simplifies to
4(2x - 9) = 3 x 4
8x - 36 = 12
18
Example 3
If you multiply both sides by 3 what is the result?
8x - 1 = 4
19
Fill in the Blanks
Type answer...
20
Multiple Select
Which equations are equivalent to 4 = 6 - 9x?
8=12−18x
20=30−45x
12=18−12x
2=4−7x
40=60−9x
Equivalent Equations
Objective: create and identify equivalent equations.
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