1. Topic 1: Solving equations and inequalities

2. 1-2 Solving linear equations
Homework:
2, 5-8, 10-12, 16-22

3. Warm up
3) =? = = = 10 8 = 5 4 5) =? = = = 71 30
4) 6 8 ∙ 1 2 =?
6 8 ∙ 1 2 = 6∙1 8∙2 = 6 16 = 3 8
6) ∙ 1 6 =?
11 5 ∙ 1 6 = 11∙1 5∙6 = 11 30

4. In this Chapter I can… 1-1: Add and multiply fractions and use PEMDAS
1-2: Create and solve linear equations with one variable on one side
1-3: Solve linear equations with one variable on both sides
1-4: Rearrange literal equations that have multiple variables

5. Examples 2(𝑥+4) 3 −8=32 Method One 2(𝑥+4) 3 =40 2 𝑥+4 =120 𝑥+4=60 𝑥=56
Method Two
2(𝑥+4) 3 =40
2 𝑥+4 =120
2𝑥+8=120
2𝑥=112
𝑥=56

6. Examples
If a kayak costs $15 per hour to rent, and has a $25 fee at the beginning, create an equation for the total cost to rent a kayak per hour. Define your variables!
Variables
C = total cost to rent a kayak
h = number of hours rented
C = 15h +25
C = 15(2) +25 = = 55
How much will it cost to rent the kayak for 2 hours?
$55 for 2 hours

7. Examples
The sum of 3 consecutive numbers is 132. What are the integers?
x = first number
x + 1 = second number
x + 2 = third number
first number + second number + third number = 132
x + x x + 2 = 132
3x + 3 = 132
3x = 129
x = 43
43 = first number
44 = second number
45 = third number

8. Warm-up
The sum of 3 consecutive odd numbers is 75. What are the integers?
x = first number
x + 2 = second number
x + 4 = third number
first number + second number + third number = 132
x + x x + 4 = 75
3x + 6 = 75
3x = 69
x = 23
23 = first number
25 = second number
27 = third number

9. 1-2 Solving linear equations
Homework:
4, 9, 23-25, 38, 39, 43

10. Example
Mr. Trimble buys some concert tickets for himself and 3 friends. He got a discount of $15 per ticket. If Mr. Trimble spent $312, how much did each ticket originally cost? Define your variables.
a = ticket original cost ($)
4 𝑎−15 =312
4𝑎−60=312
4𝑎=372
𝑎=93
𝑎−15=78
𝑎=93 or

11. Examples
Mr. Trimble runs 2.5 miles from his house to his friend’s house. His running speed is 6 mph. He then hangs out there for 45 min before walking home. His walking speed is 4 mph. How long is Mr. Trimble out?
𝑡𝑖𝑚𝑒= 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑟𝑎𝑡𝑒
Time = time running + time hanging out + time walking
Time =
Time = hours = minutes

12. 1-2 Solving linear equations
Homework:
Additional practice WKS

13. examples
Mr. Trimble is opening a pink lemonade stand. He needs 40 L of lemonade that is 20% lemonade mix and 80% water. Unfortunately, he only has a bunch of lemonade that is 15% mix and some other lemonade that is 30% mix. How many liters of the 15% lemonade and 30% lemonade should Mr. Trimble combine?
Variables
x = liters of 15% lemonade
40 – x = liters of 30% lemonade
Amount of Lemonade + Amount of Lemonade = Amount of Lemonade
Amount of Mix + Amount of Mix = Amount of Mix
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑀𝑖𝑥=𝐿𝑖𝑡𝑒𝑟𝑠∙% 𝑀𝑖𝑥
𝑥 −𝑥 0.3 =40 0.2
0.15𝑥+12−0.3x=8
−0.15𝑥=−4
𝑥=27
27 L of 15% lemonade
13 L of 30% lemonade