Download Lesson 10-11.notebook

Lesson 10­11.notebook
September 28, 2015
Lesson 10/11:
Mod 1 Topic C
True and False Equations and their Solutions Objectives
To understand that an equation is a statement of equality between two expressions
To determine that when values are substituted for the variables, the equation is either TRUE or FALSE
To find values to assign to the variables in an equation to make the equation a true statement
To understand that the commutative, associative and distributive properties as identities
WARM UP:
Read each of the following carefully and be ready to discuss the following:
• Is the statement a grammatically correct sentence? • What is the subject of the sentence? • What is the verb in the sentence? • Finally, is the sentence true? “The President of the United States is a United States citizen.” True yes!
“The President of France is a United States citizen.” “2 + 3 = 1 + 4.” True yes!
“2 + 3 = 9 + 4." Yes but false Yes but false Lesson 10­11.notebook
September 28, 2015
Recall the definition(s).
A number sentence is a statement of equality between two numerical expressions It is true if both numerical expressions are equivalent (that is, both evaluate to the same number). It is said to be false otherwise. True and false are called truth values. Determine whether the following number sentences are TRUE or FALSE. Exercise 1 Dist. prop too
59.... infinite so False
Lesson 10­11.notebook
September 28, 2015
Exercise 2
a. Could a number sentence be both TRUE and FALSE?
b. Could a number sentence be neither TRUE nor FALSE? A number sentence is either
TRUE or FALSE (and not both).
Number values on either side either match or they don't!
Important Definition:
Algebraic Equation is a statement of equality between two expressions
Algebraic equations can be number sentences
(when both expressions are numerical), but often they contain symbols whose values have not been determined.
Lesson 10­11.notebook
September 28, 2015
Not # sentence­ Has a variable
How set notation works:
The curly brackets { } indicate we are denoting a set. A set is essentially a collection of things, e.g., letters, numbers, cars, people. When elements are listed, they are listed in increasing order.
If it is not easy to list a set, like with an inequality, we use the following: N = natural = counting # {Variable symbol | # type, description}
Example: { x| x is an element of N, x> 10}
Stating what type of number the variable symbol represents is called stating its domain.
Lesson 10­11.notebook
September 28, 2015
Sometimes, a set is empty; it has no elements. In which case, the set looks like { }. We often denote this with the symbol, . We 0
refer to this as the empty set or null set. Sometimes, a set is all real numbers! It has infinite # of elements. In which case, the set is {ALL REAL NUMBERS}. We often denote this with the symbol, . R
Let's complete the chart
z = ­3
z2 = 25
6z = 3
3 in the set of real #s
The set of real #s that are 5 and ­5.
any real # not equal to 1/2
{z | z is real z = 1/2}
Z = 5Z means 1 = 5 so z < ­1
3z=2z+1z
The set of real #s that are less than or equal to ­1.
Lesson 10­11.notebook
September 28, 2015
Important Definitions:
The Solution Set of an equation written with only one variable is the set of all values one can assign to that variable to make the equation a true statement.
Solution to the Equation is any one of those values
To "Solve an Equation" means to "find the solution set" for that equation and can be written in words, with set notation or graphically.