1. EQUATIONS AND INEQUALITIES A2H CH 1 APPENDIX

2. Whole: 0, 1, 2, 3….. Integers: Whole numbers negative and positive. … -2, -1, 0, 1, 2, 3… Rational Numbers: Can be written as a fraction. Either terminates or repeats. Irrational Numbers: Can not be written as a fraction. Goes on forever without repeating. Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

3.  Classify each of the following. e.-5f. g. -4.8h. INTEGER RATIONAL IRRATIONAL Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

4. Graph the real numbers, -1.8,, and -.25 and then order them from least to greatest. -23 -3 012 -.25 -1.8 -1.8, -.25,, and. Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

5. Use the symbol to show the relationship. b.-5 and -7 a.-4 and 1 -4 -7 Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

6. Example 3: Here are the record low temperatures for five Northeastern states. Write the temperatures in increasing order. Connecticut-32  F Maine-48  F Maryland-40  F Which states have record lows below -40  F? New Jersey-34  F Vermont-50  F Maine and Vermont Vermont, Maine, Maryland, New Jersey, and Connecticut Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

7. Let a, b, and c be real numbers. PropertyAdditionMultiplication CLOSUREa + b is a real numberab is a real number COMMUTATIVEa + b = b + aab = ba ASSOCIATIVE(a + b) + c = a + (b + c)(ab)c = a(bc) IDENTITYa + 0 = a, 0 + a = aa  1 = a, 1  a = a INVERSEa + (-a) = 0a  (1/a) = 1 (a ≠0) The following property involves both addition and multiplication. DISTRIBUTIVEa(b+ c) = ab + ac Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

8. INVERSE PROPERTY of ADDITION COMMUTATIVE PROPERTY of ADDITION INVERSE PROPERTY of MULTIPLICATION ASSOCIATIVE PROPERTY of ADDITION IDENTITY PROPERTY of MULTIPLICATION Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

9.  State the property. a. 8 + -8 = 0b. 91 = 9 c. ab = bad. 8 + (2 + 6) = (8 + 2) + 6 INVERSE addition ASSOCIATIVE addition COMMUTATIVE multiplication IDENTITY multiplication Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

10. The opposite (or additive inverse) of any number a is –a. The reciprocal (or multiplicative inverse) of any nonzero number a is 1/a. Subtraction is defined as adding the opposite. Division is defined as multiplying by the reciprocal. Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

11. VOCABULARY ADDITION + SUBTRACTION - MULTIPLICATION X DIVISION ÷ SUMDIFFERENCEPRODUCTQUOTIENT Decreased by Divided by Of Less Than More ThanMinus Times Increased by For each of these operations, use the numbers in the same order they appear in the problem The only exception is LESS THAN. When writing a mathematical expression using LESS THAN, use the numbers in reverse order. Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

12. a.The difference of -3 and -15 is: b.The quotient of -18 and 2 is -9: c. Eight less than a number is twelve. -3 + 15 = 12 = -9 Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

13. Writing the units of each variable in a real-life problem is called unit analysis. It helps you to determine the units for the answer. Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

14.  Give the answer with the appropriate unit of measure. a.685 feet + 225 feet b. c. d. 910 feet 2.25 dollars per pound 135 km 45 miles per hour Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

15. You are exchanging $500 for French francs. The exchange rate is 6 francs per dollar. Assume that you use other money to pay the exchange fee. a.How much will you receive in francs? b.When you return you have 270 francs left. How much can you get in dollars? Assume that you use other money to pay the exchange fee. Real Numbers & Number Operations A2H CH 1 Equations and Inequalities MENU

16. Exponents can be used to represent repeated multiplication. EXPONENT 2 5 = 2  2  2  2  2 = BASE FACTORS An exponent tells you how many times the base is used as a factor. Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU

17. Evaluate the power. b. -3 4 a. (-3) 4 (-3)(-3)(-3)(-3) = 81 -3333 = -81 Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU

18. An order of operations helps avoid confusion when evaluating expressions. P E MD AS P Parenthesis. Compute everything inside the parenthesis. E Exponents. Evaluate powers. MD Multiplication/Division. Multiply and divide from left to right AS Addition/Subtraction. Add and subtract from left to right. Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU

19. Evaluate using order of operations. a. b.c. d. e. Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU 312 19 2 125 -7.5

20. Evaluate using order of operations. e. Evaluate 2x 3 + 3x 2 – x + 27 when x = -4 2(-4) 3 + 3(-4) 2 – -4 + 27 = -49 -4(-3) 2 + 6(-3) – 5 = -59 d. Evaluate -4x 2 + 6x – 5 when x = -3 Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU

21. Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU Consider the expression 5x 3 – 2x + 9. The parts that are added or subtracted together (5x 3, -2x, and 9) are called terms. The numbers if front of the variables (5 and -2) are called coefficients of the variables. When a term is only a number, it is called a constant (9). Terms such as 5x 3 and -7x 3 are like terms because they have the same variable part. Constant terms such as -6 and 4 are also like terms. You can only combine (add or subtract) like terms. To combine like terms, add or subtract the coefficients and leave the variable and its exponent the same.

22. Simplify the expression. a. -10(8 – y) – (4 – 15y)b. 4 – 3(x – 9) – (x + 1) c. 3x + 10 – 12x – (-4) d. 3(x – 2) – 5x(x – 8) Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU 25 - 84y-4x + 30 -9x + 14 5x 2 + 43x - 6

23. Evaluate the following expression for the given values: Algebraic Expressions & Models A2H CH 1 Equations and Inequalities MENU

24. Solving Linear Equations A2H CH 1 Equations and Inequalities MENU

25. Solving Linear Equations A2H CH 1 Equations and Inequalities MENU

26. Solving Linear Equations A2H CH 1 Equations and Inequalities MENU

27. Solving Linear Equations A2H CH 1 Equations and Inequalities MENU If the perimeter is 153, find the length of each side

28. Rewriting Equations & Formulas A2H CH 1 Equations and Inequalities MENU Solving Literal Equations: A Literal Equation is an equation with more than 1 variable We frequently manipulate literal equations when working with formulas, or changing an equations “form”. Examples

29. Rewriting Equations & Formulas A2H CH 1 Equations and Inequalities MENU Find the value for y in this equation when x is 3. Now, complete this table: XY 9 12 -4 61 -3.8 When you are asked to do something like this, it is usually easier to change the equation.

30. Rewriting Equations & Formulas A2H CH 1 Equations and Inequalities MENU This equation is written in standard form. Rewrite it in slope-intercept form. (solve for y) Now, complete this table: XY 9 12 -4 61 -3.8 18 0 96 -294 94.8

31. Rewriting Equations & Formulas A2H CH 1 Equations and Inequalities MENU Solve the equation for the indicated variable.

32.  a. You have $55 to buy digital video discs (DVDs) that cost $12 each. Write an expression for how much money you have left after buying n discs. Evaluate the expression when n = 3 and n = 4. VERBAL MODEL LABELS ALGEBRAIC MODEL –  Price per DVD Amount to Spend Number of DVDs bought –  12 dollars per DVD 55 dollars n DVDs 55 – 12n Problem Solving A2H CH 1 Equations and Inequalities MENU

33. a. Write an expression for the total monthly cost of phone service if you pay a $5 fee and 8¢ per minute. Find the cost if you talk 6 hours during the month. VERBAL MODEL LABELS ALGEBRAIC MODEL +  Price per minute Initial Fee Number of Minutes + .08 dollars per minute 5 dollars n Minutes 5 +.08n Problem Solving A2H CH 1 Equations and Inequalities MENU

34. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX ABRIDGED ALGEBRA I INEQUALITY NOTES:

35. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX Tougher inequality problems: Solve and graph:

36. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX Tougher inequality problems: Solve and graph:

37. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX Tougher inequality problems: Solve and graph:

38. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX Tougher inequality problems: Solve and graph: 3-part inequalities must be “AND”

39. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX Tougher inequality problems: What’s wrong with this:

40. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX Tougher inequality problems: Solve and graph: No solution

41. Linear Inequalities A2H CH 1 Equations and Inequalities MENUAPPENDIX Tougher inequality problems: Solve and graph: ALL REAL NUMBERS

42. Absolute Value Equations & Inequalities A2H CH 1 Equations and Inequalities MENU ABRIDGED ALGEBRA I Absolute Value NOTES:

43. Absolute Value Equations & Inequalities A2H CH 1 Equations and Inequalities MENU Solve this absolute value inequality: NO SOLUTION

44. Absolute Value Equations & Inequalities A2H CH 1 Equations and Inequalities MENU Solve this absolute value inequality: ALL REAL NUMBERS

45. A2H CH 1 Equations and Inequalities MENU OPENERS ASSIGNMENTS EXTRA PROBLEMS APPENDIX

46. A2H CH 1 Equations and Inequalities MENUAPPENDIX Properties of equality Evaluate Absolute Value Inequality Literal Equations Ordering Numbers Simplify Solve (with fractions) Solve Absolute Value Inequality

47. Properties of addition and multiplication Identify the property illustrated: Inverse Property (addition) Associative property (addition) Identity property (addition) Identity property (multiplication) Inverse property (multiplication) Distributive Property A2H CH 1 Equations and Inequalities MENUAPPENDIX Closure property (addition)

48. Evaluate the following for the values x=4 and y=9 A2H CH 1 Equations and Inequalities MENUAPPENDIX

49. SOLVE FOR X HOME A2H CH 1 Equations and Inequalities MENUAPPENDIX

50. Write this equation in function form (solve for y) A2H CH 1 Equations and Inequalities MENUAPPENDIX

51. 11. Write the following numbers in increasing order: HOME A2H CH 1 Equations and Inequalities MENUAPPENDIX

52. Simplify the following. A2H CH 1 Equations and Inequalities MENUAPPENDIX

53. SOLVE FOR X. A2H CH 1 Equations and Inequalities MENUAPPENDIX

54. SOLVE FOR X. A2H CH 1 Equations and Inequalities MENUAPPENDIX

55. Write an absolute value inequality to describe the following scenario: 15. On the Eisenhower expressway (I-290), you must drive at least 45 mph but less than 65 mph. The average of the extremesThe tolerance (difference between the average and extremes) HOME A2H CH 1 Equations and Inequalities MENUAPPENDIX

56. One of these inequalities is NO SOLUTION, the other is ALL REAL NUMBERS, can you identify which one is which? HOME A2H CH 1 Equations and Inequalities MENUAPPENDIX ALL REAL NUMBERS NO SOLUTION