Concept Byte: More Algebraic Properties

Use With Lesson 3-3

The following properties can help you understand algebraic relationships.

Reflexive, Symmetric, and Transitive Properties of Equality

For all real numbers a, b, and c:

Transitive Property of Inequality

For all real numbers a, b, and c, if a < b eh less than b  and b < c , b less than c comma  then a < c . eh less than c .

Examples

If 8 x < 7 8 x less than 7  and 7 < y , 7 less than y comma  then 8 x < y . 8 x less than y .

If 1  cup  < 1  qt  1 , cup , less than 1 , qt  and 1  qt  < 1  gal  , 1 , qt , less than 1 , gal , comma  then 1  cup  < 1  gal  . 1 , cup , less than 1 , gal , .

Example

Use the property given in parentheses to complete each statement.

1. If 7 x < y 7 x less than y  and y < z + 2 , y less than z plus 2 comma  then 7 x < 7 x less than  _____. (Transitive Property of Inequality)

   If 7 x < y 7 x less than y  and y < z + 2 , y less than z plus 2 comma  then 7 x < z + 2 . 7 x less than z plus 2 .

2. If 2000 lb = 1 ton, then 1 ton = ?. (Symmetric Property)

   If 2000 lb = 1 ton, then 1 ton = 2000 lb.

Exercises

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 and 7 = 5 + 2, then x = 5 + 2.
4. If math class is earlier than art class and art class is earlier than history class, then math class is earlier than history class.
5. Complete the following sentence. If Amy is shorter than Greg and Greg is shorter than Lisa, then Amy is shorter than _ ? . modified under bar with question mark above , .

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