1. OPENING: EXPLAIN HOW TO SOLVE A ONE- STEP EQUATION. Two-Step Equations 3.1 LESSON

2. Two-Step Equations 3.1 LESSON Add or Subtract the constant from both sides of the equation. Multiply or Divide the Coefficient to solve. Check the answer.

3. Two-Step Equations 3.1 LESSON SOLUTION x 2 – 14 8 = x 2 – 8 = Original equation Add 14 to each side to undo addition. Multiply each side by 2 to undo division. +14 x 2 2= 22 2 x = 44 Simplify. x 2 = 22 Simplify. 44 2 –14 = 8 ? Substitute 44 for x in original equation. 22 – 14 = 8

4. Two-Step Equations 3.1 LESSON – 8= 122x2x SOLUTION 4 – = – 2x2x 4 – – 2x2x = 2 – 2 – 2 = x – 8 = 122x2x – – Original equation Subtract 12 from each side to undo addition. Simplify. Divide each side by –2 to undo multiplication. Simplify. – 8= 122x2x

5. Two-Step Equations 3.1 LESSON Solve the equation. Check your answer. 13=11+ y 3 SOLUTION = y 6 Check Substitute 6 for x in original equation. 13=11+ 6 3 ? 1311= + 2 ? 13= Simplify. Add.

6. Two-Step Equations 3.1 LESSON Solve the equation. Check your answer. SOLUTION x = –3 – 6x6x + 5=23 Check Substitute – 3 for x in original equation. Simplify. Add. 18 ? 5 23 = ? =5 ? 6 + = (– 3 )

7. Two-Step Equations 3.1 LESSON Music Club You pay $9.95 to join an Internet music club. You pay $.99 for each song that you download. Your cost for joining and downloading some songs is $17.87. How many songs did you download?

8. Two-Step Equations 3.1 LESSON –9.95 0.99x7.92 = 0.99x 7.92 0.99 Write an algebraic model. Subtract 9.95 from each side to undo addition. Simplify. Divide each side by 0.99 to undo multiplication. Simplify. x is by itself. ANSWERYou downloaded 8 songs. = 17.87 9.95 + 0.99x

9. You pay $35 in dues to a photo club and $10 per roll you have developed. If you spend $225 during the year, how many rolls of film do you have developed? Use 10x + 35 = 225 and solve for x. ANSWERYou developed 19 rolls of films. Two-Step Equations 3.1 LESSON

10. CLOSING: SOLVE 11 – 4P = -1 Two-Step Equations 3.1 LESSON

11. OPENING: EXPLAING WHAT IT MEANS TO DISTRIBUTE AND COMBINE LIKE TERMS. GIVE EXAMPLES. Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON

12. Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON Solve 8x – 21 + 5x = –15. 8x – 21 – 5x = –15 8x – 5x – 21 = –15 3x – 21 = –15 + 21 +21 3x = 6 x = 2

13. Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON Solve 3a + 3 – 8a = 18. 3a + 3 – 8a = 18 3a – 8a + 3 = 18 –5a + 3 = 18 – 3 – 3 –5a = 15 a= -3

14. Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON Solve 10y – (4y + 8) = –20 10y + (–1)(4y + 8) = –20 10y + (–1)(4y) + (–1)( 8) = –20 10y – 4y – 8 = –20 6y – 8 = –20 + 8 6y = –12 y = –2 6 6y = –12

15. Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON Solve –2(3 – d) = 4 –2(3 – d) = 4 (–2)(3) + (–2)(–d) = 4 –6 + 2d = 4 + 6 2d = 10 d = 5 2 2d = 10

16. Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON Solve 4(x – 2) + 2x = 40 4(x – 2) + 2x = 40 (4)(x) + (4)(–2) + 2x = 40 4x – 8 + 2x = 40 6x – 8 = 40 + 8 6x = 48 x = 8 6 6x = 48 4x + 2x – 8 = 40

17. CLOSING: Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON

18. Solving Equations Having Parentheses Having Like Terms and Parentheses 3.2 LESSON 1.) 6 - 7x = - 15 2.) 8 + 6x - x = 8 3.) 4(3x - 9) = - 180 4.) - 2(7x - 4) = - 48 5.) A bicycle rental shop charges $5 per hour plus a fee of $10 each time you rent a bicycle. Write an equation that will illustrate the number of hours you can rent a bicycle for $45. Solve the equation.

19. OPENING: 8x + 7 = -6x – 9 DO NOT SOLVE, BUT IDENTIFY THE LIKE TERMS ON OPPOSITE SIDES OF THE EQUAL SIGN. Solving Equations with Variables on Both Sides 3.3 LESSON

20. Solving Equations with Variables on Both Sides 3.3 LESSON To solve an equation with variables on both sides, use inverse operations to "collect" variable terms on one side of the equation. Helpful Hint Equations are often easier to solve when the variable has a positive coefficient. Keep this in mind when deciding on which side to "collect" variable terms.

21. Solving Equations with Variables on Both Sides 3.3 LESSON Solve 7n – 2 = 5n + 6. 7n – 2 = 5n + 6 –5n 2n – 2 = 6 2n = 8 + 2 n = 4

22. Solving Equations with Variables on Both Sides 3.3 LESSON Solve 4b + 2 = 3b. 4b + 2 = 3b –3b b + 2 = 0 b = –2 – 2 – 2

23. Solving Equations with Variables on Both Sides 3.3 LESSON Solve 4b + 2 = 3b. 4b + 2 = 3b –3b b + 2 = 0 b = –2 – 2 – 2

24. Solving Equations with Variables on Both Sides 3.3 LESSON Solve 4 – 6a + 4a = –1 – 5(7 – 2a). 4 – 6a + 4a = –1 –5(7 – 2a) 4 – 6a + 4a = –1 –5(7) –5(–2a) 4 – 6a + 4a = –1 – 35 + 10a 4 – 2a = –36 + 10a +36 40 – 2a = 10a + 2a +2a 40 = 12a

25. Solving Equations with Variables on Both Sides 3.3 LESSON Solve -5(1 – 5x) + 5(-8x –2) = -4x – 8x 4(2x – 2) + 2(1- x) = 9 + x

26. Solving Equations with Variables on Both Sides 3.3 LESSON Solve 3x + 15 – 9 = 2(x + 2). 3x + 15 – 9 = 2(x + 2) 3x + 15 – 9 = 2(x) + 2(2) 3x + 15 – 9 = 2x + 4 3x + 6 = 2x + 4 –2x x + 6 = 4 – 6 – 6 x = –2

27. CLOSING: 14 + 5y = 50 – 4y Solving Equations with Variables on Both Sides 3.3 LESSON

28. OPENING: THINK OF INEQUALITY STATEMENTS USED OUTSIDE OF MATH. Solving Inequalities Using Addition and Subtraction 3.4 LESSON

29. Solving Inequalities Using Addition and Subtraction 3.4 LESSON Solve using inverse operations. Graph the solution Closed Circle Open Circle

30. Solving Inequalities Using Addition and Subtraction 3.4 LESSON Solve. Then graph the solution set on a number line. n – 7 ≤ 15 + 7 n ≤ 22 Add 7 to both sides. Draw a closed circle at 22 then shade the line to the left of 22. -44 -220 224466 –88-66

31. Solving Inequalities Using Addition and Subtraction 3.4 LESSON Solve. Then graph the solution set on a number line. a – 10 ≥ –3 + 10 +10 a ≥ 7 Add 10 to both sides. Draw a closed circle at 7. Then shade the line to the right. –4 –2 0 2 4 6 8 10

32. Solving Inequalities Using Addition and Subtraction 3.4 LESSON Solve. Check each answer. d + 11 > 6 –11 d > –5 Check d + 11 > 6 0 + 11 > 6 11 > 6 Subtract 11 from both sides. 0 is greater than –5. Substitute 0 for d.

33. Solving Inequalities Using Addition and Subtraction 3.4 LESSON Solve. Check your answer. b + 12 ≤ 19 –12 b 7 Check b + 12 ≤ 19 6 + 12 19 18 < 19 Subtract 12 from both sides. 6 is less than 7. Substitute 6 for b. ≤ ?

34. Solve. Then graph each solution set on a number line. 1. x – 4 > 17 2. z – 27 ≤ 19 Solve. Check each answer 3. p + 18 ≥ –6 Solving Inequalities Using Addition and Subtraction 3.4 LESSON

35. Solving Inequalities Using Multiplication and Division 3.5 LESSON Solve using inverse operations. Graph the solution Closed Circle Open Circle SPECIAL RULE: when you multiply or divide both sides by a negative number, flip the inequality symbol.

36. Solving Inequalities Using Multiplication and Division 3.5 LESSON Solve. c4c4 ≤ –4 c4c4 ≤ (–4)(4) c ≤ –16 Multiply both sides by 4. c4c4

37. Solving Inequalities Using Multiplication and Division 3.5 LESSON Solve. r > 9 r –3 >9 r < (–3)9 (–3) r < 27 –3 Multiply both sides by –3 and reverse the inequality symbol.

38. Solving Inequalities Using Multiplication and Division 3.5 LESSON Solve. Check your answer. 192< -24b 192 < 24b –24 -8 > b Divide both sides by –24, and reverse the inequality symbol.

39. Solving Inequalities Using Multiplication and Division 3.6 LESSON Solve. Check your answer. 85 < -17b 85 < 17b –17 -5 > b Divide both sides by –17, and reverse the inequality symbol.

40. CLOSING: Solve and Graph a – 5 > 3 -3 < b + 7 Solving Inequalities 3.4 LESSON

41. OPENING: DESCRIBE A TIME WHEN YOU TRIED TO BREAK A RECORD. Solving Inequalities Multi-Step Inequalities 3.6 LESSON

42. Solving Inequalities Multi-Step Inequalities 3.6 LESSON Solve the inequality and graph the solutions. 45 + 2b > 61 –45 2b > 16 b > 8 0246810 12 14 16 18 20

43. Solving Inequalities Multi-Step Inequalities 3.6 LESSON 8 – 3y ≥ 29 –8 –3y ≥ 21 y ≤ –7 –10 –8 –6–4 –2 0246810 –7 Solve the inequality and graph the solutions.

44. Solving Inequalities Multi-Step Inequalities 3.6 LESSON Solve the inequality and graph the solutions. –4(2 – x) ≤ 8 −4(2 – x) ≤ 8 −4(2) − 4(−x) ≤ 8 –8 + 4x ≤ 8 +8 4x ≤ 16 x ≤ 4 –10 –8 –6–4 –2 02468 10

45. Solving Inequalities Multi-Step Inequalities 3.6 LESSON Solve the inequality and graph the solutions. y ≤ 4y + 18 –y 0 ≤ 3y + 18 –18 – 18 –18 ≤ 3y –6 ≤ y (or y  –6) –10 –8 –6–4 –2 0246810

46. Solving Inequalities Multi-Step Inequalities 3.6 LESSON 4m – 3 < 2m + 6 –2m – 2m 2m – 3 < + 6 + 3 2m < 9 4 5 6 Solve the inequality and graph the solutions.

47. Solving Inequalities Multi-Step Inequalities 3.6 LESSON Solve the inequality and graph the solutions. 5t + 1 < –2t – 6 +2t 7t + 1 < –6 – 1 < –1 7t < –7 7 t < –1 –5 –4 –3–2 –1 01234 5

48. CLOSING: WHAT MUST YOU DO WITH THE VARIABLE IF THE EQUATION HAS VARIABLES ON BOTH SIDES OF THE EQUATION? Solving Inequalities Multi-Step Inequalities 3.6 LESSON