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**Summary Subsets of Real Numbers**

EQ: How do you identify and use properties of real numbers?

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**The maximum speed of a roller coaster is given by the formula s = .**

Roller Coaster Play Video (1.7 MB) The maximum speed of a roller coaster is given by the formula s = .

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**Summary Subsets of Real Numbers (R)**

Natural numbers (N) are the numbers used for counting. Whole numbers (W) are the natural numbers and 0.

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Integers The integers (Z) are the natural numbers (positive integers), zero, and the negative integers. Each negative integer is the opposite, or additive inverse, of a positive integer.

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Rational Numbers Rational numbers (Q) are all the numbers that can be written as quotients of integers. Each quotient must have a nonzero denominator. Some rational numbers can be written as terminating decimals. For example, 1/8= All other rational numbers can be written as repeating decimals. For example, 1/3 = . 3

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Irrational Numbers Irrational numbers (I) are numbers that cannot be written as quotients of integers. Their decimal representations neither terminate nor repeat. If a positive rational number is not a perfect square such as 25 or 4/9, then its square root is irrational.

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** Subsets of Real Numbers**

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**Homework Page 6 Exercises 7-23 odd **

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Order of Operations How do you use the order of operations to simplify algebraic expressions?

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**Get your computer! www.mathisfun.com**

Click on algebra, then click on order of operations. Read the through the examples on the website, then take the eight question quiz.

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**Mistakes There is a mistake in each of the following problems.**

Discover what was done incorrectly. -20 is correct. 2 ¼ is correct. 17 is correct.

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Homework

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Solving Equations

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Vocabulary A number that makes the equation true is a solution of an equation.

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**Solving an Equation with a Variable on Both Sides**

Solve 13y + 48 = 8y − 47.

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You Try Solve 8z + 12 = 5z – 21 z = -11 Solve 2t – 3 = 9 – 4t t = 2

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**Using the Distributive Property**

Solve 3x − 7(2x − 13) = 3(−2x + 9)

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You Try Solve 6(t – 2) = 2(9 – 2t) t = 3

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**Solving a Formula for One of Its Variables**

Geometry: The formula for the area of a trapezoid is A = h(b1 + b2). Solve the formula for h.

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**Your Turn Solve the formula for the area of a trapezoid for b1.**

A = ½h(b1 + b2)

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**Solving an Equation for One of Its Variables**

Solve ax +10 = bx + 3 for b.

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Your Turn Solve ax + bx – 15 = 0 for a.

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**Real-World Connection**

Construction A dog kennel owner has 100 ft of fencing to enclose a rectangular dog run. She wants it to be 5 times as long as it is wide. Find the dimensions of the dog run.

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Your Turn A rectangle is twice as long as it is wide. Its perimeter is 48 cm. Find its dimensions. x = 8

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Homework Worksheet

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Review/Quiz

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Solving Inequalities EQ: What are the differences between solving equations and solving inequalities?

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Vocabulary A solution of an inequality in one variable is any value of the variable that makes the inequality true. Most inequalities have many solutions. The graph of a linear inequality in one variable is the graph on the real number line of all solutions of the inequality.

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**Solving and Graphing Inequalities**

Solve the inequality. Graph the solution. -3x – 12 < 3

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Your Turn Solve 3x – 6 < 27. Graph the solution. x <11

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**Solving and Graphing Inequalities**

Solve the inequality. Graph the solution. 6 + 5(2 – x) ≤ 41

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Your Turn Solve 12 > 2(3x + 1) Graph the solution. x < -2

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**No Solutions or All Real Numbers as Solutions**

Solve each inequality. Graph the solution. 2x – 3 > 2(x – 5)

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**No Solutions or All Real Numbers as Solutions**

Solve each inequality. Graph the solution. 4(x – 3)+7 ≥ 4x +1

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Your Turn Solve 2x < 2(x + 1) + 3. Graph the solution.

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Real World Connection A band agrees to play for $200 plus 25% of the ticket sales. Write an inequality to model the situation. The solve the inequality to determine the ticket sales needed for the band to receive at least $500. $200+25%>500

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Homework Page 41 Exercises 11, 14, 15-18, 21-26, 41

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**Solving Compound Inequalities**

EQ: How do you solve and graph a compound sentences and inequalities using and and or?

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Vocabulary A compound inequality is a pair of inequalities joined by and or or. To solve a compound inequality containing and, find all values of the variable that make both inequalities true.

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**Compound Inequality Containing And**

Graph the solution of 3x − 1 > −28 and 2x + 7 < 19.

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**Compound Inequality Containing And**

Graph the solution of -2x + 3 < 4x +2 and -2x +3> -4x - 2

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**Compound Inequality Containing And**

Graph the solution of 5 < -2x + 1/2 < 27/3.

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Your Turn Graph the solution of 2x > x + 6 and x – 7 < 2.

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**Compound Inequality Containing Or**

Graph the solution of 4y − 2 ≥ 14 or 3y − 4 ≤ −13.

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**Compound Inequality Containing Or**

Graph the solution of 3x + 1 < 7 or 2x - 9 > 7.

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**Compound Inequality Containing Or**

Graph the solution of -3 ≤ 2y + 9 or 18 > 4y – 10.

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Your Turn Solve x – 1 < 3 or x + 3 > 8. Graph the solution.

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Ticket Out Graph given the solution set is {x|x > 4 and x > 2}, then graph given the solution set is {x|x > 4 or x > 2} . Compare the two graphs, what is your conclusion?

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Homework x + 7 > -2 or x - 4 < 8 Page 41 Exercises 27-38

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Day 2 Homework: Page Exercises 12, 13, 19-20, 27-38, 40.

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**Solving Absolute Value Equations**

EQ: How do you solve an absolute value equation?

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**Definition of Absolute Value**

The absolute value of a number is its distance from zero on the number line and distance is nonnegative. For any real number a: If a ≥ 0, then |a| = a If a < 0, then |a| = -a So, the absolute value of a negative number, such as -5, is its opposite, -(-5) or 5.

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**Solving Multi-Step Absolute Value Equations**

Solve |4x – 1| – 5 = 10

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Example Solve |x – 3 | + 2 = 4

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Example

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No Solution Solve |2x + 3| +10 = 5

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Examples Solve -2|x – 3| = 12 Solve -5|x +1|= -8

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Your Turn 1) |3x + 2| = 7 2) 2|3x – 1| + 5 = 33

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Work in Pairs Write an absolute value equation for your partner to solve, then check one another’s work.

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Homework Page 47 Exercises 5-18

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**1.8 Solving Absolute Value Inequalities**

EQ: How do you solve and graph absolute value inequalities?

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**Absolute Value Inequalities**

Let k represent a positive real number. |x| ≥ k is equivalent to x ≤ -k or x ≥ k. |x|≤ k is equivalent to x ≤ k and x ≥- k (-k ≤ x ≤ k) Hint: greatOR -- greater is an or less thAND-- less than is an and

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**Solving Inequalities of the Form |x|≥b**

Solve |3x + 6|≥ 12. Graph the solution.

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**Solving Inequalities of the Form |x|≥b**

Solve |6 – 2x | + 4 ≥ 40. Graph the solution.

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**Solving Inequalities of the Form |x|<b**

Solve |2x – 3|< 3 . Graph the solution.

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**Solving Inequalities of the Form |x|<b**

Solve |2x + 3| < -2. Graph the solution.

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**Solving Inequalities of the Form |x|<b**

Solve ½ |2x + 3| < 8. Graph the solution.

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**Solving Inequalities of the Form |x|<b**

Solve 3|2x + 6| - 9 < 15. Graph the solution.

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Homework Page 47 Exercises 19-34

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Review/Test

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Section 1.8 Homework questions?. Section Concepts 1.8 Linear Equations in Two Variables Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission.

Section 1.8 Homework questions?. Section Concepts 1.8 Linear Equations in Two Variables Slide 2 Copyright (c) The McGraw-Hill Companies, Inc. Permission.

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