1. Label individual bell ringers by date
Which of the following mathematical expressions is equivalent to the verbal expression “A number, x, squared is 39 more than the product of 10 and x”? F. 2x = x G. 2x = 39x + 10x H. x2 = 39 – 10x J. x2 = 39 + x10 K. x2 = x
Note: Write all bell ringers from a given week on a single piece of paper. Turn this piece of paper in on the last day of the week.
Title: Bell Ringers
Label individual bell ringers by date

2. 1.2 Properties of Real Numbers
In this class there are real numbers and imaginary numbers, for the first 5 units we will only deal with real numbers!
We will always start with vocabulary. Only write vocabulary terms you DO NOT know.

3. Subsets of Real Numbers
Natural Numbers Ex. 1, 2, 3, 4 … The numbers used for counting

4. Subsets of Real Numbers
Whole Numbers Ex. 0, 1, 2, 3, 4 … The natural numbers and 0

5. Subsets of Real Numbers
Integers Ex. … -3, -2, -1, 0, 1, 2, 3 … The natural numbers, their opposites, and zero

6. Subsets of Real Numbers
Rational Numbers Ex. 7/5, -3/2, -4/5, 0, 0.3, -1.2, 9 Any number that can be written as a quotient; any number that terminates or repeats

7. Subsets of Real Numbers
Irrational numbers Ex. √2, √7 , √2/3, … Numbers that cannot be written as quotients of integers

8. Subsets of Real Numbers
This diagram represents how all the subsets are related.

9. Graphing numbers on the number line
To be able to graph on a number line you need to understand what integers numbers fall between Practice: Name the 2 numbers each number falls between -3/2 = -2 ¼ = …. =

10. The opposite or additive inverse of any number a is –a
The opposite or additive inverse of any number a is –a. The sum of opposites is 0.
Practice:
⅙ =
-⅝ =
-(-3.2) =

11. The reciprocal or multiplicative inverse of any nonzero a is 1/a
The reciprocal or multiplicative inverse of any nonzero a is 1/a. The product of reciprocals is 1.
Practice:
⅙ =
-⅝ =
-(-3.2) =

12. Finding Absolute Value
The absolute value of a real number is its distance from zero on the number line. Practice: Find |-4|, |0|, and |-1(-2)| and graph on a number line.

13. 1.3 Patterns and Expressions
Vocabulary: A variable is a symbol, usually a letter, that represents one or more numbers. Ex. x, y, a, b….

14. Vocabulary continued …
Algebraic Expression or a Variable Expression: an expression that contains one or more variables Ex. 3x + 2b *Note: An expression has no equation sign!!!!

15. Vocabulary continued …
Evaluate: When you substitute numbers for the variables in an expression and follow the order of operations to simplify Practice: a – 2b + ab for a = 4 and b = -2

16. Evaluating Practice
–x2 + 3(x – 3) for x = 2

17. x(4x – x) – x2 for x = -5 and x = -2
Evaluating Practice
x(4x – x) – x2 for x = -5 and x = -2

18. Term: A number, a variable, or the product of a number and one or more variables
Coefficient: The numerical factor in a term
5x2 + 6x

19. Like terms = the same variables raised to the same powers Ex
Like terms = the same variables raised to the same powers Ex. 3x2 and 5x2 or -7x3 and 8x3

20. Combining like terms
Practice:
5x2 – 10x + 3x2
-(m + n) + 2(m – 3n)

21. Finding the perimeter by combining like terms3x
2x - y y 2x y
3x - y

22. Practice
Evaluate the expression for the given values of the variables. 4a + 7b + 3a – 2b + 2a; a = -5 and b=3

23. Practice
Evaluate the expression for the given value of the variable. |x| + |2x| - |x – 1|; x = 2

24. Evaluate |2x + 3| + |5 – 3x|for x = -3

25. Equations with variables on both sides
1.4 Solving Equations
Solve 13y + 48 = 8y - 47
Equations with variables on both sides

26. Practice
8x + 12 = 5x - 21

27. Practice
2x – 3 = 9 – 4x

28. Using the Distributive Property
3x – 7(2x – 13) = 3(-2x + 9)

29. Practice
2(y – 3) + 6 = 70

30. Practice
6(x – 2) = 2(9 – 2x)

31. Solving a Formula for One of it’s Variables
Solve the formula for the area of a trapezoid for h: A = ½ h (b1 + b2)

32. Solve the same equation for b1
A = ½ h (b1 + b2)

33. Homework Study vocabulary terms used in todays class
Review sections 1 – 3 from Chapter 1 in your textbook if you need the extra practice

34. Solving an Graphing Inequalities
1.5 Solving Inequalities
Solving an Graphing Inequalities
3x – 12 < 3

35. Practice
6 + 5(2 – x) < 41

36. Practice
12 > 2(3x + 1) + 22

37. Solve each inequality and graph the solution. 2x – 3 > 2(x – 5)
Special Cases
Solve each inequality and graph the solution. 2x – 3 > 2(x – 5)

38. Solve each inequality and graph the solution. 7x + 6 < 7(x – 4)
Special Cases
Solve each inequality and graph the solution. 7x + 6 < 7(x – 4)

39. Real World Connection
Revenue: A band agrees to play for $200 plus 25% of the ticket sales. Find the ticket sales needed for the band to receive at least $500. Write an inequality and solve:
x > 500
x > 1200

40. Practice
A salesperson earns a salary of $700 per month plus 2% of the sales. What must the sales be if the salesperson is to have a monthly income of at least $1800?
at least $55,000

41. Compound Inequalities (AND)
A compound inequality is a pair of inequalities joined by AND or Or. Example: 3x – 1 > -28 and 2x + 7 < 19

42. Practice (AND)
2x > x + 6 and x – 7 < 2

43. Compound Inequalities (OR)
4y – 2 > 14 or 3y – 4 < -13

44. 1.6 Absolute Value Equations and Inequalities
The absolute value of a number is its distance from zero on the number line and distance is nonnegative. Example: |2x – 4| = 12

45. Practice
|3x + 2|= 7

46. Solving Multi-Step AV Equations
3|4x – 1| - 5 = 10

47. Practice
2|3x – 1| + 5 = 33

48. Practice
|2x + 7| = -2

49. An extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation

50. Checking for extraneous Solutions
|2x + 5| = 3x + 4
Solve like normal
Check your answers

51. Practice
|2x + 3| = 3x + 2

52. Solving Absolute Value Inequalities
Solve |3x + 6| > 12. Graph the solution.

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

54. Solve |5x + 3| - 7 < 34 . Graph the solution.
Practice
Solve |5x + 3| - 7 < 34 . Graph the solution.

55. Bell Ringer The expression (3x – 4y2)(3x + 4y2) is equivalent to:

56. Bell Ringer
The expression -8x3(7x6 – 3x5) is equivalent to: A. -56x9 + 24x8 B. -56x9 - 24x8 C. -56x x15 D. -56x18 – 24x15 E. -32x4

57. Bell Ringer
Marlon is bowling in a tournament and has the highest average after 5 games, with scores of 210, 225, 254, 231, and 280. In order to maintain this exact average, what must be Marlon’s score for his 6th game? F. 200 G. 210 H. 231 J. 240 K. 245