1-6 Identity and Equality Properties

							                      Drill #8*
Find the solution set for each open sentence if the
    replacement set is {-3, -½, 0, 1, 3}. Substitute each
    value in each equation. Show your work.


1. 4x = x + 3

2. 2x – 3 < 1

3.   x 9  0
      2
       1-6 Identity and Equality
              Properties


Objective: To recognize and use the properties
of identity and equality, and to determine the
multiplicative inverse of a number.
   Additive Identity Property**
Definition: For any number a,
            a+0=0+a=a

Every operation has an identity. It is the
 number that allows the another number to
 keep its identity when the operation is
 performed. That means that the other
 number does not change.
Multiplicative Identity Property**
Definition: For any real number a,
            a(1) = (1)a = a.

Notice that when we perform the operation
 (multiplication) on a, a remains the same,
 it keeps its identity.
  Multiplicative Property of 0**
Definition: For any real number a,
            a(0) = (0)a = 0.

When we multiply 0 times anything we get 0.

What happens when we divide something
 into 0? When we divide 0 into something?
 Why?
   Multiplicative Inverse Property**
                                       a
Definition: For every non-zero number b, where
                                       b
  a,b = 0, there is exactly one number a
              a b
  such that b ( a )  1
The multiplicative inverse of a number is its reciprocal.

Examples:
Name the multiplicative inverse:
a. 5      b. x         c. ½         d. - ¾
 Reflexive property of equality**
Definition: For any real number a, a = a.

This is the basic property of equality. All
 other properties of equality stem from this.
    Symmetric Property of Equality**
Definition: For all real numbers a and b, if a = b
 then b = a.

Example:
    if y = 5x + 2 then 5x + 2 = y
Transitive Property of Equality**
Definition: For all real numbers a, b, and c,
 if a = b, and b = c, then a = c.

Example:
 if x = y and we know that y = 6 then we
 also know that x = 6.
 Substitution Property of Equality**
Definition: If a = b, then a may be replaced
 by b.

Example:
 if x + 5 = 2y + 1 and we know that x = 6,
 then we can replace x with 6.
 6 + 5 = 2y + 1
       Roosevelt High Pep Club
The pep club at Roosevelt High School is selling
 submarine sandwiches, lemonade, and apples
 at the district swim meet. Each sandwich costs
 $2.00 to make and sells for $3.00. Each glass
 of lemonade costs $0.25 to make and sells for
 $1.00. Each apples costs the club $0.25, and
 the members have decided to sell apples for
 $0.25 each. Write an expression that
 represents the profit for 80 sandwiches, 150
 glasses of lemonade, and 40 apples…