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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. 092 x
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**
Definition: For every non-zero number , where
a,b = 0, there is exactly one number
such that
The multiplicative inverse of a number is its reciprocal.
Examples:
Name the multiplicative inverse:
a. 5 b. x c. ½ d. - ¾
a
b
1)( a
b
b
a
b
a
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…
