Algebra 1 Common Core Student Edition, Grade 8-9

Concept Byte

Use W ith Lesson 3-3

More Algebraic

Properties

Common Core State Standards

Prepares for A-REI.B.3 Solve linear equations and

inequalities in one variable, including equations w ith

coefficients represented by letters.

MP 2

The following properties can help you u n d e rsta n d algebraic relationships.

Reflexive, Symmetric, and Transitive Properties of Equality

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For all real n um bers a, b, a n d c:

Reflexive Property

a = a

Examples

5x = 5x, $1 = $1

Symmetric Property

If a = b, then b = a. If 15 = 31, then 3t = 15.

If 1 pair = 2 socks, th e n 2 socks = 1 pair.

Transitive Property

If a = b and b = c, then a = c. If d = 3y and 3y = 6 , t h e n d = 6.

If 36 in. = 3 ft a n d 3 ft = 1 yd, th e n 36 in. = 1 yd.

Transitive Property of Inequality

For all real n u m b ers a, b, and c,ifa< b and b < c, then a < c.

Examples If 8x < 7 and 7 < y, then 8 x < y.

If 1 cup < 1 q t an d 1 qt < 1 gal, th e n 1 cup < 1 gal.

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Ex a m p l e

Use the property given in parentheses to complete each statement.

0 If 7 x< y an d y < z + 2, then 7x<M. (Transitive P roperty of Inequality)

If 7x y and y z H- 2 ; th a n 7x ^ z “I- 2.

0 If 2000 lb = 1 ton, th e n 1 to n = (Sym m etric Property)

If 2000 lb = 1 ton, th e n 1 to n = 2000 lb.

Ex e r c i se s

Name the property that each statement illustrates.

1. If 3.8 = n, then n = 3.8. 2. 6 in. = 6 in. 3. If x = 7 a n d 7 = 5 + 2, th e n x = 5 + 2.

4. If m ath class is earlier th a n art class an d art class is earlier th a n history class, th e n
   m ath class is earlier th a n history class.


5. C om plete th e following sentence. If Amy is sh o rter th a n Greg an d Greg is shorter
   th a n Lisa, th e n Amy is sh o rter th a n?.

184 Concept Byte More Algebraic Properties