Jag Nation Pride When you enter this classroom, immediately do the following: 1.Take your seat. 2.Turn off all electronic devices and place in backpack.

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Jag Nation Pride When you enter this classroom, immediately do the following: 1.Take your seat. 2.Turn off all electronic devices and place in backpack. 3.Take out all necessary materials (planner, binder, pencil) and place back pack on floor under desk. 4.Read the Smart Board and follow all directions posted. Copy homework assignment into planner. 5.Use a white board to complete any bell work that is assigned.

BELLWORK

Lesson 11 Solution Sets for Equations and Inequalities

STUDENT OUTCOME The student will…. understand that an equation with variables is viewed as a question asking for the set of values one can assign to the variables of the equation to make the equation a true statement. Students understand the commutative, associative, and distributive properties as identities; e.g., equations whose solution sets are the set of all values in the domain of the variables. Homework: pgs R even H even

CLASSWORK (page S.54) Example 1: Consider the equation,, where represents a real number. a. Are the expressions and algebraically equivalent? b. The following table (S. 54) shows how there is a true value that would make the equation true. There is 1 more value, can you find it?

CLASSWORK Example 2: Consider the equation THE NUMBER SENTENCETRUTH VALUE Let p = = 12 FALSE Let p = 4 Let Let p = 5

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. Any one of those values is said to be a solution to the equation. To solve an equation means to find the solution set for that equation. Example 3: Solve for One can describe a solution set in any of the following ways: IN WORDS: has solutions 5 and -5. IN SET NOTATION: The solution set of is {-5, 5}. IN A GRAPHICAL REPRESENTATION ON A NUMBER LINE:

Exercise 1: (page S. 56) Solve for a: Present the solution set in words, in set notation, and graphically. Words: Set Notation: Graphically:

Exercise 2: Depict the solution set of in words, in set notation, and graphically. Words: Set Notation: Graphically:

Example 4: (page S.56) Using the table provided, solve for for x, over the set of positive real numbers. Depict the solution set in words, in set notation, and graphically. Words: Set Notation: Graphically:

Exercise 3: (page S.57)

Example 5: Solve for x:

Exercise 4: Solve for a: Describe the solution set in words, in set notation, and graphically. Words: Set Notation: Graphically:

Exercise 5: (page S.58) Identify the properties of arithmetic that justify why each of the following equations has a solution set of all real numbers: (using commutative, associative, distributive) a. b. c.

Exercise 6: Create an expression for the right side of each equation such that the solution set for the equation will be all real numbers. (There is more than one possibility for each expression. Feel free to write several answers for each one.) a. = ___________________ b. = ___________________ c. = ________________ d. = _ ___________________

EXIT TICKET 1. Here is the graphical representation of a set of real numbers: a. Describe this set of real numbers in words. b. Describe this set of real numbers in set notation. c. Write an equation or an inequality that has the set above as its solution set. 2. Indicate whether each of the following equations is to have a solution set of all real numbers. Explain your answers for each. a. b.