1. Chapter 7
Pre-Algebra

2. Bell Ringer Width: 𝒘 Length: 𝒘+𝟏𝟎 Equation: 𝟒𝒘+𝟐𝟎=𝟏𝟎𝟎
Get out yesterday’s homework assignment (7.4)
Think of any clarifying questions you may have about
Write an equation for the following word problem:
The perimeter of the classroom is 100 feet. The length is 10 feet greater than the width. Find the length and the width.
Width: 𝒘
Length: 𝒘+𝟏𝟎
Equation: 𝟒𝒘+𝟐𝟎=𝟏𝟎𝟎

3. Quiz Review

4. QUIZ TOMORROW!! Sections 7.1-7.4 Homework: Page 393-394, 8-23 Study:
Notes
Problems from today’s review

5. Bell Ringer (7.5)
Get out your notebook and prepare to take notes on Section 7.5
Prepare to ask questions about the quiz

6. 7.5 – Solving Equations With Variables on Both Sides (Page 371)
Essential Question:
How is solving an equation with the variable appearing twice on the same side of the equals sign different from solving an equation with the variable appearing on both sides of the equals sign?

7. 7.5 cont.
Steps in Solving Equations 1. Remove ( ) 2. Remove fractions or decimals by multiplication 3. Combine like terms 4. Isolate variables to one side 5. Undo + or - 6. Undo x or / 7. Check!!
4. Isolate variables to one side

8. 7.5 cont.
Example 1:
3𝑦−20=8𝑦
−3𝑦
−3𝑦
−20=5𝑦 5 5
−4=𝑦
CHECK!!

9. 7.5 cont.
Example 2:
𝑞+𝑞+𝑞=𝑞+6
3𝑞=𝑞+6 −𝑞 −𝑞
2𝑞=6 2 2
CHECK!!
𝑞=3

10. 7.5 cont. 7.5 cont. 5 𝑛−3 =2𝑛−6 5 𝑛−3 =2𝑛−6 5𝑛−15=2𝑛−6 −2𝑛 −2𝑛
Example 3:
5 𝑛−3 =2𝑛−6
Example 3:
5 𝑛−3 =2𝑛−6
5𝑛−15=2𝑛−6
−2𝑛
−2𝑛
3𝑛−15=−6
+15
+15
3𝑛=9
CHECK!! 3 3
𝑛=3

11. 7.5 cont. 6 𝑔+3 =−2 𝑔+31 6𝑔+18=−2𝑔−62 +2𝑔 +2𝑔 8𝑔+18=−62 −18 −18 8𝑔=−80
Example 4:
6 𝑔+3 =−2 𝑔+31
6𝑔+18=−2𝑔−62
+2𝑔
+2𝑔
8𝑔+18=−62
−18
−18
8𝑔=−80
CHECK!! 8 8
𝑔=−10

12. 7.5 cont.
Example 5:

13. 7.5 - Closure
How is solving an equation with the variable appearing twice on the same side of the equals sign different from solving an equation with the variable appearing on both sides of the equals sign?
Twice on same side:
Combine terms using the operation shown
On both sides:
Combine terms using inverse operations

14. Page , 4-22 even, 28, 30
7.5 - Homework

15. 𝒙>𝟒 Bell Ringer (7.6) Get out your 7.5 homework assignment
Get out your notebook and prepare to take notes on Section 7.6
Solve the following equation for x: 2𝑥>8
𝒙>𝟒

16. 7.6 – Solving Two- Step Inequalities (Page 377)
Essential Question:
How is solving two-step inequalities different from solving two-step equations?

17. 7.6 cont. = ≤, ≥ = <, > Graphing Inequalities:
We can use the number line to solve inequalities containing < , ≤ , > , and ≥ .
= ≤, ≥
= <, >

18. 7.6 cont. 2𝑦−3≤−5 +3 +3 2𝑦≤−2 2 2 𝐲≤−𝟏 Example 1:
Solve and graph 2𝑦−3≤−5.
2𝑦−3≤−5 +3 +3
2𝑦≤−2 2 2
𝐲≤−𝟏

19. 7.6 cont. −5𝑦+3≥28 −3 −3 −5𝑦≥25 −5 −5 𝒚≤−𝟓 Example 2: Solve −5𝑦+3≥28.
**Remember to reverse the direction of the inequality symbol when you multiply or divide by a negative number**

20. Therefore, the greatest number of rides Dale can ride is 14.
7.6 cont.
Example 3:
Dale has $25 to spend at a carnival. If the admission to the carnival is $4 and the rides cost $1.50 each, what is the greatest number of rides Dale can go on?
1.5x+4≤25
Therefore, the greatest number of rides Dale can ride is 14. −4 −4
1.5𝑥≤21
1.5
1.5
𝒙≤𝟏𝟒

21. 7.6 - Closure
How is solving two-step inequalities different from solving two-step equations?
Same except when you multiply or divide each side of an inequality by a negative number, you must also reverse the inequality symbol.

22. 7.6 - Homework
Page 379, 4-24 even, 34, 35

23. Bell Ringer (7.7) −𝟔𝒚+𝟑≥𝟐𝟕 −𝟔𝒚≥𝟐𝟒 𝒚≤−𝟒
Get out your 7.6 homework assignment
Get out your notebook and prepare to take notes on Section 7.7
Solve the following inequality for y: −6𝑦+3≥27
−𝟔𝒚+𝟑≥𝟐𝟕
−𝟔𝒚≥𝟐𝟒
𝒚≤−𝟒

24. 7.7 – Transforming Formulas (Page 382)
Essential Question:
What does it mean to “solve a formula for a given variable”?

25. NOT THE RACE CAR BRENDEN!!
7.7 cont.
Formula:
An equation that shows a relationship between quantities that are represented by variables
NOT THE RACE CAR BRENDEN!!
BEITZ RACING

26. 7.7 cont. 𝐴=𝑙𝑤 𝑤 𝑤 𝐴 𝑤 =𝑙 Transforming in One Step:
Example 1: Solve the area formula for length.
𝐴=𝑙𝑤 𝑤 𝑤
𝐴 𝑤 =𝑙

27. 7.7 cont. 𝑃=2𝑙+2𝑤 −2𝑙 −2𝑙 𝑃−2𝑙=2𝑤 2 2 1 2 𝑃−𝑙=𝑤
Transforming in More Than One Step:
Example 2: Solve the perimeter formula for width.
𝑃=2𝑙+2𝑤
−2𝑙
−2𝑙
𝑃−2𝑙=2𝑤 2 2
1 2 𝑃−𝑙=𝑤

28. 7.7 cont. Transforming Temperatures:
Example 3: Convert 32℃ to ℉ by solving 𝐶= 5 9 𝐹−32 for F, then substituting.
𝑪= 𝟓 𝟗 𝑭− 𝟏𝟔𝟎 𝟗
𝑭= 𝟗 𝟓 𝑪+𝟑𝟐
𝑪+ 𝟏𝟔𝟎 𝟗 = 𝟓 𝟗 𝑭
𝑭= 𝟗 𝟓 𝟑𝟐 +𝟑𝟐
𝟗𝑪+𝟏𝟔𝟎=𝟓𝑭
𝑭= 𝟐𝟖𝟖 𝟓 +𝟑𝟐
𝑭= 𝟗 𝟓 𝑪+𝟑𝟐
𝑭=𝟖𝟗.𝟔

29. 7.7 - Closure
What does it mean to “solve a formula for a given variable”?
Expressing one variable in terms of the other variables used in the formula

30. 7.7 - Homework
Page 384, 4-26 even

31. Bell Ringer (7.8) Get out your 7.7 homework assignment
Get out your notebook and prepare to take notes on Section 7.8
What does the term “interest” mean in mathematics?

32. 7.8 – Simple and Compound Interest (Page 386)
Essential Question:
What is the difference between simple interest and compound interest?

33. 7.8 cont.
New Vocabulary:
Principal – initial amount of an investment or loan
Interest - fee charged by a lender to a borrower for the use of borrowed money
Interest Rate – percentage of the balance that an account or investment earns in a fixed period of time

34. 7.8 cont.
New Vocabulary:
Simple Interest – interest paid only on the principal

35. 7.8 cont. 𝐼=𝑝𝑟𝑡 𝐼= 1000 .06 2 𝐼=120= ONLY INTEREST!!
Example 1:
Suppose you deposit $1,000 in a savings account that earns 6% interest per year. Find the interest earned in 2 years. Find the total principal plus interest.
SIMPLE INTEREST PROBLEM!!
𝐼=𝑝𝑟𝑡 𝐼=
𝐼=120= ONLY INTEREST!!
$1,000+$120=$1,120

36. 7.8 cont. Balance – principal plus earned interest
Interest Period – length of time over which interest is calculated
Can be a year or less than a year

37. 7.8 cont.
Compound Interest – interest paid on both the principal and the interest earned in previous interest periods

38. 7.8 cont. OR 𝐵=𝑝 1+𝑟 𝑛 $𝟓𝟗𝟎.𝟗𝟖 𝐵=400 1+.05 8 𝐵=486.2 1+.05 4 𝐵=590.98
Example 2:
Suppose you deposit $400 in an account that earns 5% interest compounded annually. The balance after the first four years is $ What is the balance in your account after another 4 years, a total of 8 years?
COMPOUND INTEREST PROBLEM!!
𝐵=𝑝 1+𝑟 𝑛 𝐵=
𝐵=590.98 𝐵=
𝐵=590.98 OR
$𝟓𝟗𝟎.𝟗𝟖

39. 7.8 cont.

40. $𝟐𝟖𝟏𝟔.𝟐𝟑 7.8 cont. 𝐵=𝑝 1+𝑟 𝑛 𝐵=2500 1+.015 8 𝐵=2816.23 Example 3:
Find the balance on a deposit of $2,500 that earns %3 interest compounded semiannually for 4 years.
𝐵=𝑝 1+𝑟 𝑛 𝐵= 𝐵=
$𝟐𝟖𝟏𝟔.𝟐𝟑

41. 7.8 cont.

42. 7.8 - Closure
What is the difference between simple interest and compound interest?
Simple Interest:
Paid only on the principal
Compound Interest:
Paid on both the principal and the previously earned interest

43. 7.8 - Homework
Page 389, 2-18 even

44. Bell Ringer Get out your 7.8 homework assignment
Think of any clarifying questions you may have about Chapter 7
Find the balance on a deposit of $1000 that earns 4% interest compounded semiannually for 5 years.

45. Steps for Solving Equations:
1. Remove ( )
2. Remove fractions or decimals by 𝒙
3. Combine like terms
4. Isolate variables to one side
5. Undo + or −
6. Undo × or ÷
7. Check!!

46. 7.1 - Review (Page 393)

47. 7.2, Review (Page 393)

48. 7.4 - Review (Page 394)

49. 7.5 - Review (Page 394)

50. 7.6 - Review (Page )

51. 7.7 - Review (Page 347)

52. 7.8 - Review (Page 395)

53. 7.8 – Review cont. (Page 395)

54. TEST TUESDAY!! Sections 7.1-7.8 Homework: Page 396, 2-42 even Study:
Notes
Problems from today’s review