Download presentation

Published byCara Shearer Modified over 3 years ago

1
**Chapter 1: Expressions, Equations, & Inequalities**

Sections 1.3 – 1.6

2
**1.3 Algebraic Expressions**

Algebraic Expression: contains numbers, variables, and mathematical signs (no equal sign) Equation: contains numbers, variables, mathematical signs, and an EQUAL SIGN

3
**1.3 Algebraic Expressions**

Write an algebraic expression 1. one less than the product of six and w 6w – 1

4
**1.3 Algebraic Expressions**

2. You are on a bicycle trip. You travel 52 miles on the first day. Since then, your average rate has been 12 miles per hour. What algebraic expression models the distance traveled? Let h be the number of hours traveled. h

5
**1.3 Algebraic Expressions**

Evaluate the following expressions 3. 2r + 5(s+6) – 1 if r = 3, s = – 9 2(3) + 5(– 9+6) – 1 2(3) + 5(–3) – 1 6 + – 15 – 1 – 9 – 1 – 10

6
**1.3 Algebraic Expressions**

4. c³ - d/8 if c = ¼ , d = 1 (¼)³ – 1/8 1/64 – 1/8 1/64 – 8/64 – 7/64

7
**1.3 Algebraic Expressions**

5. Tickets to a museum are $8 for adults, $5 for children, and $6 for seniors a.) What algebraic expression models the total number of dollars collected in ticket sales? 8a + 5c + 6s

8
**1.3 Algebraic Expressions**

b.) If 20 adults, 16 children, and 10 senior tickets are sold one morning, how much money is collected in all? 8(20) + 5(16) + 6(10) 300

9
**1.3 Algebraic Expressions**

Simplify 6. 2a² + 3b² + 6b² + 5a² 7a² + 9b²

10
**1.3 Algebraic Expressions**

7. –(x + 4y) + 5(3x – y) – x – 4y + 15x – 5y 14x – 9y Assign pgs: 22 – 23, #10 – 19, 20 – 26 even, – 44 even, 52 (23 problems)

11
**1.4 Solving Equations Reflexive: a = a Symmetric: if a = b then b = a**

Transitive: if a = b and b = c, then a = c Addition: if a = b then a + c = b + c Subtraction: if a = b then a - c = b – c Multiplication: if a = b then a(c) = b(c) Division: if a = b then a ÷ c = b ÷ c

12
**1.4 Solving Equations Solve the following equations 1. x – 8 = -10**

x = – 2

13
**1.4 Solving Equations 2. – 2(y – 1) = -16 + y – 2y + 2 = – 16 + y**

18 = 3y y = 6 Assign Pg. 23 – 24, #53, 55, 63 – 66 Pg. 30, #10 – 24 even (14 problems)

14
**1.4 Solving Equations Cont’d**

Solve x -6 = 6x – 5 – x 5x – 5 = 5x – 5 – 5x – 5x – 5 = – 5 which means… infinite number of solutions or all real numbers

15
**1.4 Solving Equations Cont’d**

2. –x + 2(5x – 1) = 2(3x+4) + x – x + 10x – 2 = 6x x 9x – 2 = 7x + 8 – 7x – 7x 2x – 2 = 8 2x = 10 x = 5

16
**1.4 Solving Equations Cont’d**

3. What is t in terms of A in A = 1000(1+0.05t) A = t – – 1000 A – 1000 = 50t t = A – 20 50

17
**1.4 Solving Equations Cont’d**

4. Solve A = ½ (b + c) for b 2(A) = 2 (½)(b + c) 2A = b + c – c – c 2A - c = b b = 2A – c Assign pgs: 30–31, #28 – 36, 38, 41, 42, 46, 48, 49, 61 16 problems

18
**1.5 Part 1 Solving Inequalities**

Transitive: if a > b and b > c, then a > c Addition: if a > b then a + c > b + c Subtraction: if a > b then a - c > b – c Multiplication: if a > b and c > 0 then a(c) > b(c) if a > b and c < 0 then a(c) < b(c) Division: if a > b and c > 0 then a ÷ c > b ÷ c if a > b and c < 0 then a ÷ c < b ÷ c

19
**1.5 Part 1 Solving Inequalities**

*If you multiply or divide by a negative number, FLIP THE ARROW! Graphing: mean open dots >, < mean closed dots ≥, ≤

20
**1.5 Part 1 Solving Inequalities**

Graph x > 3. Graph 3 < x. Graph 4 < x. 3 3 4

21
**1.5 Part 1 Solving Inequalities**

1. Solve the inequality and graph the solution. 4(x – 7) > −20 4x – 28 > –20 4x > 8 x > 2 2

22
**1.5 Part 1 Solving Inequalities**

2. 4(−n – 2) – 6 >18 – 4n – 8 – 6 > 18 – 4n – 14 > – 4n > 32 – 4 – 4 n < – 8 −8

23
**1.5 Part 1 Solving Inequalities**

Solve. (x + 3) ≥ 4(2 + x) 3x + 9 ≥ 8 + 4x – 3x – 3x 9 ≥ 8 + x 1 ≥ x which can also be written as x ≤ 1 Assign pgs.38-40: #14-23 all, 68,69,71-78 all Reminder: QUIZ (1.3 – 1.4) TOMORROW!!!! 1

24
**1-5 Part 2 Solving Inequalities**

4. What inequality represents the sentence? 5 fewer than the product of seven and a number is no more than 50. 7n – 5 < 50

25
**1-5 Part 2 Solving Inequalities**

What inequality represents the sentence? The quotient of a number and 6 is at least 10.

26
**1-5 Part 2 Solving Inequalities**

5. −½(y + 3) ≥ 1/3y – 4 Retype this in Equation Editor new year.

27
**1-5 Part 2 Solving Inequalities**

5 (cont’d) y ≤ 3

28
**1-5 Part 2 Solving Inequalities**

5 (cont’d) y < 3 Assign pgs 38 – 39: # all, 24,27,45,46 8 problems

29
**1-5 Part 2 Solving Inequalities**

5. −½(y + 3) ≥ 1/3y – 4 –3y – 9 ≥ 2y – 24 –2y –2y

30
**1-5 Part 2 Solving Inequalities**

5 (cont’d) –5y – 9 ≥ – –5y ≥ –15 y ≤ –3 Assign pgs 38 – 39: # all, 24,27,45,46 8 problems

31
**1-5 Part 3 Solving Inequalities**

Solve – x – 5 < -x + 4 – x + 4 < – x + 4 + x x 4 < 4 which means… No Solution

32
**1-5 Part 3 Solving Inequalities**

Solve – x – 5 ≤ − x + 4 – x + 4 ≤ – x + 4 + x x 4 ≤ 4 which means… All Real Numbers

33
**1-5 Part 3 Solving Inequalities**

Compound Inequality: Two inequalities joined together by the word “and” or the word “or”

34
**1-5 Part 3 Solving Inequalities**

“and” The solution must be true for both inequalities at the same time. (usually shades in the middle)

35
**1-5 Part 3 Solving Inequalities**

8. ½a < 3 and – 3a + 5 < 8 – 3a + 5 < 8 −5 −5 – 3a < 3 – 3 – 3 a > – 1 2(½a) < 2(3) a < 6 a < 6 and

36
**1-5 Part 3 Solving Inequalities**

8. (cont’d) ½a < 3 and – 3a + 5 < 8 Smallest number a < 6 and a > − 1 This is the solution!! – 1 < a a < 6 − 1 6

37
**1-5 Part 3 Solving Inequalities**

“or” The solution will make any or all parts of the inequalities true. (usually shades to the outside)

38
**1-5 Part 3 Solving Inequalities**

9. ½a > 3 or – 3a + 5 > 8 a > 6 or a < − 1 All of this is the solution!!! − 1 6

39
**1-5 Part 3 Solving Inequalities**

Now try these problems on your own! Solve and graph. 10. 5x ≥ −15 and 2x < 4 −2x > 10 or x + 6 ≥ 7 Assign: p #29-43 odd, 47

40
**1-5 Part 4 Solving Inequalities**

12. 1 < 2x + 3 < 9 − 3 − 3 − 3 − 2 < 2x < − 1 < x < 3 − 1 3

41
**1-5 Part 4 Solving Inequalities**

Assign: p #28-42 even, 55,59,67

42
**1.6 Absolute Value Equations**

the distance from 0 on a number line │5 │= 5 │−5 │= 5 Notice that either a number OR its opposite have the same absolute value.

43
**1.6 Absolute Value Equations**

To Solve Absolute Value Equations: Get the absolute value on a side by itself. Set the expression inside the absolute bars equal to its value (the number on the other side). Set the opposite of the expression inside the absolute bars equal to its value (the number on the other side). Solve and check.

44
**1.6 Absolute Value Equations**

1. Solve. |x| = 5 x = 5 − x = 5 − 1 − 1 x = −5 SOLUTION x = 5,− 5 x = ± 5

45
**1.6 Absolute Value Equations**

Solve. 2. │2x + 5 │= 9 2x + 5 = 9 2x = 4 x = 2 −(2x + 5) = 9 −2x − 5 = 9 − 2x = 14 x = − 7 x = 2, −7

46
**1.6 Absolute Value Equations**

3. ½│2x − 4 │ − 2 = 6 ½│2x − 4 │= 8 2 ∙ (½│2x − 4 │) = 2 ∙ (8) │2x − 4 │= 16 Continued on next slide…

47
**1.6 Absolute Value Equations**

3. continued │2x − 4 │= 16 − (2x – 4) = 16 −2x + 4 = 16 −2x = 12 x = −6 2x – 4 = 16 2x = 20 x = 10 x = 10, − 6

48
**1.6 Absolute Value Equations**

|3x| = −9 3x = − 9 x = − 3 − 3x = −9 x = 3 NO SOLUTION!!! WHY ???????????

49
**1.6 Absolute Value Equations**

Assignment pgs.46 #10 – 18 all, 22

50
**Less than (and) Greater (or)**

1-6 Part 2 (Abs. Value) Less than (and) Greater (or) an an er or

51
**1-6 Part 2 (Abs. Value) x < 5 AND ‒x < 5 x < 5 AND x > − 5**

52
**1-6 Part 2 (Abs. Value) x > 5 OR − x > 5 x < − 5 x > 5 OR**

53
**1-6 Part 2 (Abs. Value) OR x < −8 OR x > 2 7. 2│2x + 6 │+ 6 ≥ 26**

−(2x + 6) > 10 −2x − 6 > 10 −2x > 16 x < −8 2x + 6 > 10 2x > 4 x > 2 x < −8 OR x > 2 2 −8

54
**1-6 Part 2 (Abs. Value) − 2 < x x < ½ 8. Solve and graph.**

4x + 3 < 5 4x < 2 x < ½ AND − (4x + 3) < 5 − 4x − 3 < 5 − 4x < 8 x > − 2 − 2 < x x < ½ −2 1/2

55
1-6 Part 2 (Abs. Value) Assignment: pgs.46 #23, 25 – 36 all

Similar presentations

OK

1 hi at no doifpi me be go we of at be do go hi if me no of pi we Inorder Traversal Inorder traversal. n Visit the left subtree. n Visit the node. n Visit.

1 hi at no doifpi me be go we of at be do go hi if me no of pi we Inorder Traversal Inorder traversal. n Visit the left subtree. n Visit the node. n Visit.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on human nutrition and digestion article Ppt on regional trade agreements Download ppt on earthquake in india Ppt on history of cricket for class 9 Short ppt on social networking sites Ppt on natural and artificial satellites around earth Ppt on forward contracts Ppt on economic order quantity formula Ppt on instrument landing system for sale Ppt on 600 mw generator