Section 2-4
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Transcript of Section 2-4
![Page 1: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/1.jpg)
Section 2-4
Reasoning with Properties from
Algebra
![Page 2: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/2.jpg)
Properties of Equality
![Page 3: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/3.jpg)
Addition property
202
2182
x
x
•Adding something to each side of an equation
Given+ 18 + 18 Therefore, the
Addition Property of (=) was applied.
Example:
![Page 4: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/4.jpg)
subtraction property
2182
23185
x
xxx3
•Subtracting from each side of an equation
Givenx3 Therefore, the
Subtraction Property of (=) was applied.
Example:
![Page 5: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/5.jpg)
Multiplication property
35
57
s
s
•Multiplying something to each side of an equation
Example:Given7 7
Therefore, the Multiplication Property of (=) was applied.
![Page 6: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/6.jpg)
division property•Dividing something on each side of an equation
Example:
20
402
x
x Given
2 2Therefore, the Division Property of (=) was applied.
![Page 7: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/7.jpg)
Reflexive property• Same exact thing on each
side of the equal sign!
ABAB Examples:
44 3232
![Page 8: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/8.jpg)
Symmetric property• The sides of an equation are
switched. (Nothing else is done with the equation.)
325
532
ABCD
CDAB
Examples:
![Page 9: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/9.jpg)
Transitive property
ca
cb
ba
* Relates
to the Law of
Syllogism!
![Page 10: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/10.jpg)
Examples:
1532
155
532
EFAB
EFCD
CDAB
![Page 11: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/11.jpg)
substitution property
• Plugging in something in place of another thing in any equation or expression.
Example: 4162
42
,16
x
x
![Page 12: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/12.jpg)
Distributive property• a(b+c) = ab +ac *Helps to get rid of
parentheses
Example: 4(x+y) Given
= 4•x + 4•y
= 4x + 4y Therefore, the Distribution Property was applied.
![Page 13: Section 2-4](https://reader036.fdocuments.us/reader036/viewer/2022080916/56812d10550346895d91ebe0/html5/thumbnails/13.jpg)
Simplification• To combine like terms
Example: x= 3 + 5 Given
= 8
Therefore, the Simplification was applied.