1. -6a – 13a =-19a -8n + 14n = 6n 10r - 19r = -9r

2. 5xy + 3xy =8xy 2s 2 10ac + 19ac = 9ac 9s 2 + 11s 2 =

3. 2n x 8 = 16n 24a 2 5e x 9e =45e 2 6a x 4a =

4. 28b ÷ 7 = 4b 5 2 24 ÷ 4d =6/d 5 3 ÷ 5 =

5. x - 3.5 = 8.9 – 3x 4x =12.4 x+-3.5 = 8.93x 4x =8.9 + 3.5 x = 3.1

6. 2x + 20 = 12 X = 2x = -8 -4

7. 2/5 = 4y + 16 2/5 = y = 4y-16 -4

8. 24 + 4c = -2c = -24 4c = -2c - c = 24 6c -4

9. 1212 3 = ____ 10 22 = ______ 2 50 10110

10. 4 24 2 4 1 256 6 8 - 10 = 4 24 2 = 4 = 1 = 6262 = 6 10 6 8 = 36

11. Rename 2.025 as a mixed number Let x =.025 (x) = (.025) 10x = 0.25 10 (10x) = (0.25)100 1000x =25.25

12. Rename 2.025 as a mixed number 10x =.25 1000x = 25.25 = 990x25 x =25/900 or 1/ 36

13. Rename 2.025 as a mixed number x =25/900 or 1/ 36 2.025 = 2 +.025.025 = 1/36 2.025 = 2 1/36

14. Two-Step Inequalities OBJECTIVE:  Solve, graph, and check inequalities that call for two steps to simplify

15. 2x + 20 < 12 x < -4 2x < 12 -20 2x < -8 Graph the solution. -2 -3 -4 -5 -6 0 Check. Substitute -4 for x. 2(-4) + 20 < 12 -8 + 20 < 12 12 < 12; False Therefore, -4 is not a solution. Solve. Graph and check the solution.

16. -2 -3 -4 -5 -6 0 Check another value. 2(-6) + 20 < 12 -12 + 20 < 12 8 < 12; True Therefore, -6 is a solution. Substitute -6 for x. Try -10. 2(- 10) + 20 < 12 -20 + 20 < 12 0 < 12; True Therefore, -10 is also a solution.

17. 3a < 16 + 11a a -2 3a – 11a < 16 -8a < 16 Graph the solution. -2 -3 -4 -5 -6 0 Check. Substitute -2 for a. 3(-2) < 16 + 11(-2) -6 < 16 -22 -6 < -6;False Solve. Graph and check the solution. -8 >

18. Graph the solution. -2 -3 -4 -5 -6 0 Check. Substitute -2 for a. 3(-2) < 16 + 11(-2) -6 < 16 -22 -6 < -6; False Therefore -2 is not a solution. Substituting 0 for a. 3(0) < 16 + 11(0) 0 < 16 +0 0 < 16True Therefore 0 is a solution.

19. Homework. PB, p119-120 Class work. PB, p119

20. Multistep Inequalities with Grouping symbols OBJECTIVE:  solve, graph, and check the solution of an inequality having a grouping symbols

21. 4(x + 3) -2 Graph the solution. -6 -7 -8 -9 -10 -11 -5 Solve. Graph and check the solution. ≤ 16 Multiply both sides by -2. -2 4(x + 3) - 32 ≥ Apply the DPMoA. 4x + 12 ≥ - 32 Subtract 12 from both sides. - 12 - 11 4x ≥ Divide both sides by 4 4 4 x ≥ - 44 -4

22. Graph the solution. -6 -7 -8 -9 -10 -11 -5 -4 Check the solution. 4(x + 3) -2 ≤16 Try -11for x. 4(-11 + 3) -2 ≤16 Combine like terms. 4(-8) -2 ≤ 16 Multiply. -32 -2 16 ≤ Divide 16 ≤ True, so -11 is a solution.

23. Graph the solution. -6 -7 -8 -9 -10 -11 -5 -4 Check the solution. 4(x + 3) -2 ≤16 Try x = -5. 4(-5 + 3)3) -2 ≤16 Combine like terms. 4(-2) -2 ≤ 16 Multiply. -8 -2 16 ≤ Divide 164≤ True, so -5 is a solution.

24. HW: PB, p121-122 Class work PB, p121

25. Multistep Inequalities :fractions and decimals  solve, graph, and check the solution of an inequality having fractions and decimals objective Pp 114-115, text

26. (0.12x + 0.36) -1-2-340 Example 1.Solve. Graph and check the solution. 0.6 Multiply both sides by 100. 12 - 36 ≥ 1 100 12x + 36 ≥ 60 Subtract 36 from both sides. - 36 12x ≥ 24 Divide both sides by 12. 12 x2 ≥ Graph. 23 0.12x + 0.36 ≥ 0.6 Substitute -2 for x, then evaluate.

27. 0.12x + 0.36 ≥ 0.6 Substitute -2 for x, then evaluate. 0.12(2) + 0.36 ≥ 0.6 Multiply. 0.24 + 0.36 ≥ 0.6 Add. 0.60 ≥ 0.6 True, so 2 is a solution. 0.12x + 0.36 Try 4 for x, then evaluate. ≥ 0.6 0.12(4) + 0.36 ≥ 0.6 0.48 + 0.36 ≥ 0.6 Multiply. Add. 0.84 ≥ 0.6 True, so 4 is also a solution.

28. HW: PB, p125-126 Class work PB, p125

29. Compound inequalities OBJECTIVE:  graph and find the solution of compound inequalities pp 116-117, text

30. 1 2 3 4 5 6 0 Graph: x > 3 and x < 7. x > 3 Graph on the number line. 8 9 10 711 x < 7 Graph on the same number line. Solution. The solution set of the compound inequality in shortened form is: {x | 3 < x < 7}

31. -2 -1 0 1 2 3 -3 Graph: z ≤ -2 or z ≥ 4. z ≤ -2 Graph on the number line. 5 6 7 48 z ≥ 4 Graph on the same number line. The solution set of the compound inequality in shortened form is: {z | z ≤ -2 or z ≥ 4}

32. Homework. PB, p127-128 Class work. PB, p127

33. Polynomials OBJECTIVE:  d efine a polynomial  c lassify a polynomial by the number of its terms  s implify polynomials pp 124-125, text

34. Do You Remember? A symbol, usually a letter, used to represent a number variable Expressions that contain variables, numbers, and operation symbols Algebraic Expressions A term that doesn’t have variables constant

35. Do You Remember? It tells how many times a number or variable called the base is used as a factor. exponent A __ of an algebraic expression is a number, a variable, or the product of a number and one or more vaeiables. term

36. Remember…  A monomial is an expression that is a number, a variable, or the product of a number and one or more variables with nonnegative exponents.  examples:19, m, 7a 2, 13xy, 1/4 abc 10 MMonomials that are real numbers are called constants.

37. Remember…  A polynomial is a monomial or the sums and/or differences of two or more monomials.  Each monomial in a polynomial is called a t tt term.  Polynomials can be classified by their n nn number of terms when they are in s ss simplest form.

38. Remember… Types of P PP Polynomial NameNumber of TermsExamples Monomial Binomial Trinomial 1(mono means one) 2(bi means two) 3(tri means three) 2n, 4x 3, r, 7, 6x 2 y 5 2x + 8; 3b + p; 2a 2 – 8b 2 4n + b + c; 2x 2 + 8x - 3

39. Remember… Classifying P PP Polynomials; before classifying a a polynomial make sure it is in its simplest form. Example. Simplify: x 2 + 2x + 1 + 3x 2 – 4x. Then classify it.

40. Remember… Example. What kind of a polynomial is x 2 + 2x + 1 + 3x 2 – 4x? x 2 + 2x + 1 + 3x 2 – 4xCombine like terms. 4x 2 – 2x + 1Classify. 4x 2 – 2x + 1 is a trinomial because it has 3 terms.

41. Homework. PB, p139-140 Class work. text, p125

42. Modeling Polynomials OBJECTIVE:  u se Algebra tiles to model polynomials pp 128-129, text

43. Algebra Tiles = x 2 = -x 2 = x = -x = 1 = -1 Examples of polynomials and their models. x 2 - 4-3x 2 + 2x +1

44. Write the polynomials modeled by each set of Algebra tiles. 4x 2 + 7x-2x 2 – 2x + 9 3x 2 + 3x - 5 -3x 2 + 2x - 1

45. If a polynomial is not in simple form, model it with Algebra tiles then combine like tiles. Example. Simplify 3x 2 – 2x – 4 + x 2 + 3x. Model the polynomial. Create zero pairs, (an x tile and a –x tile, and other opposites). The simple form is 4x 2 + x – 4. Then rearrange the tiles so the like ones are next to each other.

46. Homework. PB, p143-144 Class work. text, p129

47. Add Polynomials OBJECTIVES :  m odel the addition of polynomials  a dd polynomials algebraically pp 130-131, text

48. Algebra Tiles = x 2 = -x 2 = x = -x = 1 = -1

49. Example. Add 3x 2 – 4x + 5 and 2x 2 – x – 3. 3x 2 - 4x + 5 -2x 2 - x - 3 Step 1. Model each polynomial. +

50. 2x 2 - x - 3 Step 1. Model each polynomial. 3x 2 - 4x + 3 Step 2. Put the same tiles next to each other.

51. Step 2. Put the same tiles next to each other. Step 3. Create zero pairs from opposite tiles.

52. Step 3. Create zero pairs from opposite tiles. Step 4. Name the remaining tiles for the answer. x 2 - 5x + 2

53. Example. Add 2x 2 + 11x + 9 and 3x 2 – 6x (2x 2 + 11x + 9)(3x 2 - 6x) Polynomials can be added algebraically, in either horizontal or vertical form. + To add polynomials horizontally,use the Commutative and Associative properties to group and combine like terms Remove parentheses. 2x 2 + 11x + 9 + 3x 2 - 6x Use the APA and CPA to group and combine like terms 2x 2 + 3x 2 + 11x – 6x + 9 5x 2 + 5x + 9 Answer.

54. 6x 2 - 7y 2 Example. Add 4x 2 + 3xy – 9y 2 and 6x 2 – 7y 2 4x 2 + 3xy – 9y 2 + To add polynomials vertically, arrange like terms in columns and add the columns separately. 10x 2 + - 16y 2 Arrange like terms in columns 3xy Answer.