Chapter 1 Sections 1.4

Yesterday’s Exit Slip Explain how you know  is an irrational number. It is irrational because it is neither a repeating nor a terminating decimal. Explain why natural numbers are enclosed by whole numbers, integers, and rational numbers. Natural Numbers belong in the set of whole numbers, which are in the set of integers, which are in the set of rational numbers List five rational numbers and five irrational numbers. State why the numbers are either rational or irrational. (Answers may very) Explain the difference between the commutative and associative properties. Use the commutative property when you can switch the order of the numbers around the operation without affecting the answer (“commute”). Use the associative property when you can move the parentheses or regroup the numbers in a given problem without affecting the answer (“associate”).

Objectives: To translate verbal expressions and sentences into algebraic expressions and equations. To solve equations by using the properties of equality. To solve equations for a specific variable. Use a graphing calculator to estimate solutions of equations by building tables of values.

Language of Math Verbal ExpressionExpression a number increased by 4 twice the cube of a number the square of a number decreased by the cube of the same number three times the sum of a number and 6 x + 4 2x 3 c 2 – c 3 3(b + 6) Verbal SentenceEquation Nine is equal to five plus four. A number decreased by -6 is = m – 6 = -3

Solving Equations Reflexive Property of Equality For any real number a, a = a. Symmetric Property of Equality For all real numbers a and b, if a = b, then b = a. Transitive Property of Equality For all real numbers a, b, and c, if a = b and b = c, then a = c. Substitution Property of Equation If a = b, then a may be replaced by b. Addition and Subtraction Properties of Equality For any numbers a, b, and c, if a = b, then a + c = b + c and a – c = b – c. Multiplication and Division Properties of Equality

Example Solve: 3(2a + 25) – 2(a – 1) = 78 3(2a + 25) – 2(a – 1) = 78 6a + 75 – 2a + 2 = 78 Rewrite Distributive property 4a+ 77 = 78 Addition and subtraction properties (combining like terms) 4a = 1 Subtraction property Division properties

Example The perimeter of a parallelogram is 48 inches. What is the length of the longer side if the shorter side measures 9 inches? Answer: l = 15 9 l

Example Mrs. Flaherty wants to put up new cabinets in the classroom. She needs 1.5 feet for each cabinet, and she has 10.5 feet of wall to put the cabinets on. How many cabinets can she put up? Answer: 7 cabinets

Technology Estimate the solution of 12x – 3 = 5 to the nearest hundredth. Rewrite the equation in an equivalent form to get 0 on one side. 12x – 8 = 0 On your calculator: “Y =”  Y 1 = 12x – 8 TblSet  TblStart = 0  Tbl = 1 Indpnt: Auto Dependent: Auto

Technology Table Look at the values that are there. We are looking for x when y = 0. We need to make are increments smaller. On your calculator: “Y =”  Y 1 = 12x – 8 TblSet  TblStart = 0  Tbl =.1 Indpnt: Auto Dependent: Auto What does our table look like?

Technology Keep adjusting the increment value until you can find an appropriate x value. Answer:  0.67