CHAPTER 7 Solving Equations and Inequalities
Chapter 7: Solving Equations & Inequalities 7.2 - Solving Two-Step Equations 7.4 - Circles and Circumferences QUIZ 7A: on 7.2 and 7.4 Friday 3/15 7.5 - Solving Equations with Variables of Each Side 7.6 - Solving Multi-Step Inequalities 7.7 - Writing Inequalities QUIZ 7B: on 7.5 - 7.7 Friday 3/22 7.8 - Using the Metric System TEST on Chapter 7 BLOCK 3/27 and 3/28
Chapter 7.2 Solving Two-Step Equations Objective: To solve equations that involve more than one operation
Warm-Up: P326 (1-10 ALL)
Chapter 7.2 Solving Two-Step Equations Notes: Let’s Review…What’s an equation?
“Peal the onion” or Work outside 1. 2. 3. 4.
c – 19 = 17 -3n + 8 = -7 2 + 4m = 1 3=n-3 4
in.
Chapter 7.2 Solving Two-Step Equations Your turn…
Chapter 7.2 Solving Two-Step Equations Your turn…
Chapter 7.2 Solving Two-Step Equations
p336 (6–30 x 3)
One Step Equations One-step equations with multiplication 2-step equations
7-4: Circles and Circumference Objective: To find the circumference of a circle
Warm-Up: 1. 2. 3. 4. 5. 6.
20 = 6x + 8 -10 – k = -36 2y – 7 = 15 15- 4g = - 33 2.1 = 0.8 – z -17 + = 3 36
7. 8.
- 49 =
+ 11
Answers: 1. x = 2 2. k = 26 3. y = 11 4. g = 12 5. z = - 1.3 6. t = 100 7. k = - 126 8. z = - 360
7-4: Circles and Circumference Notes:
7.4 Circles and Circumferences NOTES: Your Turn…Write the radius and then find the Circumference
Circumferences: 1. 9.42 cm 2. 25.12 mm 3. 3.14 cm 4. 12.874 dm 5. 160.328 m 6. 24.806 cm
7-4 Circles and Circumference Notes: Fun With Pie Pi Poem (First 5 digits) Pi Chain (First 5 digits) Write a story about Sir Cumference and the Round Table Cookie and Plate Challenge String and a Cup Shuffle Pi
7-4 Circles and Circumference Notes: π Sing the song “We Wish You a Happy Pi Day” by Dianna sung to the tune of We Wish You a Merry Christmas We wish you a happy Pi Day We wish you a happy Pi Day We wish you a happy Pi Day To you and to all
7-4 Circles and Circumference Notes: Sing O Number Pi: (to the tune of "Oh Christmas Tree") Oh, number Pi Oh, number Pi Your digits are unending,
one five nine, And even more if we had time,
Oh, number Pi Oh, number Pi
Oh, number Pi Oh, number Pi
No pattern are you sending. You're three point one four
For circle lengths unbending.
7-4 Circles and Circumferences
P343 (6-28 EVEN) or Three Activities
Radius diameter and circumference
7-5 Solving Equations with Variables on Each Side Objective: To solve equations with variables on each side Warm-Up: Please solve each equation 1) -5a -18= 7 2) 3+ 2b= - 7 3) 5 = 7(y – 3) – 2 4) m+5=2 3 5) If he radius is 5cm, then what is circumference?
Answers: 1) 2) 3) 4) 5)
a = -5 b = -5 y=4 m the =1 31.4 cm
7-5 Solving Equations with Variables on Each Side NOTES: What is a “Like Term”?
What differences do you see in the two lists?
7-5 Solving Equations with Variables on Each Side NOTES: Collect and ADD the “Like Terms”:
7-5 Solving Equations with Variables on Each Side NOTES:
TIME FOR A CHALLENGE! 1)
−20 = −4a − 6a
2)
10 = 1 − 2w + 5w
3)
8t − 2 = −9 + 7t
4)
4f + 3f = 7f
5)
r − 8 = −(r + 4)
6)
3(x +1) - 5 = 3x - 2
7)
12m = −4(−6m − 3) HINT :
“Null” means NO SOLUTION and it is NEVER true! “All” means ALL NUMBERS are possible to make it true!
Answers 1)a= 2 2)w = 3 3)t = -7 4)All 5)r = 4 6)Null 7)m = - ½
7-5 Solving Equations with Variables on Each Side NOTES:
7-5 Solving Equations with Variables on Each Side NOTES:
7-5 Solving Equations with Variables on Each Side
p348-349 (4-28 Even)
Equations with variables on both sides One step inequalities
7-6 Solving Multi-Step Inequalities Objective: To solve inequalities with more than one operation
1. 2. 3. 4. 5.
Warm-Up: Please solve each equation 5a – 18 = 3a -3b + 13 = -b – 3 4(2x – 1) – 3 = 5(x – 5) 7(y – 3) – 2 = 3(2y – 5) + 4 4/ m + 5 = 2/ m – 3 7 7
Answers: 1) a = 9 2) b = 8 3) x = -6 4) y = 12 5) m = -28
7-6 Solving Multi-Step Inequalities NOTES:
7-6 Solving Multi-Step Inequalities NOTES:
7-6 Solving Multi-Step Inequalities NOTES: Rule: If each side of an inequality is multiplied or divided by a negative number, the order symbol of the inequality must be reversed.
Solve b – 8 ≥ 3b – 8 and check the solution. Graph the solution on a number line. b – 8 ≥ 3b – 8 +8 +8 1. Add 8 to each side. b ≥ 3b 2. Subtract 3b from each side. – 3b – 3b 3. Divide each side by –2 –2b ≤ 0 4. And change ≥ to ≤. -2 -2 b≤0
1. 2. 3. 4. 5. 6. 7.
Solve 5m - 8 > 12 +8 +8 Draw “the river” Add 8 to both sides 5m > 20 Simplify Divide both sides by 5 5 5 Simplify Check your answer m>4 Graph the solution 5(4) – 8 = 12 3
o 4
5
1. 2. 3. 4. 5. 6. 7.
Solve 12 - 3a > 18 - 12 - 12 Draw “the river” Subtract 12 from both sides -3a > 6 Simplify Divide both sides by -3 -3 -3 Simplify (Switch the inequality!) a < -2 Check your answer Graph the solution 12 - 3(-2) = 18 -3
o -2
-1
Which graph shows the solution to: 2x - 10 ≥ 4? 1.
.
2. 3. 4.
Answer Now
Solve 5m - 4 < 2m + 11 1. 2. 3. 4. 5. 6. 7. 8. 9.
Draw “the river” Subtract 2m from both sides Simplify Add 4 to both sides Simplify Divide both sides by 3 Simplify Check your answer Graph the solution
- 2m -2m 3m - 4 < 11 +4 +4 3m < 15 3 3 m<5 5(5) – 4 = 2(5) + 11
o 4
5
6
Solve 2r - 18 ≤ 5r + 3 1. 2. 3. 4. 5. 6. 7. 8. 9.
Draw “the river” Subtract 2r from both sides Simplify Subtract 3 from both sides Simplify Divide both sides by 3 Simplify Check your answer Graph the solution
-8
-2r
-2r -18 ≤ 3r + 3 -3 -3 -21 ≤ 3r 3 3 -7 ≤ r or r ≥ -7 2(-7) – 18 = 5(-7) +3
●
-7
-6
6) Solve -2x + 6 ≥ 3x - 4 1. 2. 3. 4.
x≥ x≤ x≥ x≤
-2 -2 2 2
Answer Now
Solve 1. 2. 3. 4. 5. 6. 7. 8. 9.
Draw “the river” Subtract 14p from both sides Simplify Add 20 to both sides Simplify Divide both sides by 12 Simplify Check your answer Graph the solution
26p - 20 > 14p + 64 -14p -14p 12p – 20 > 64 + 20 + 20 12p > 84 12 12 p>7 26(7) – 20 = 14(7) + 64
o 6
7
8
What are the values of x if 3(x + 4) - 5(x - 1) < 5?
1. 2. 3. 4.
x < -6 x > -6 x<6 x>6
Answer Now
7-6 Solving Multi-Step Inequalities
p353 (6-30 EVEN)
Inequalities on a number line Multi-step linear inequalities
7.8 - The Metric System Objective: To convert measurements within the metric system Warm-Up: Solve and Graph 1. 2. 3.
21 - 4t < 25 18 + 6m > -24 - 5.72 < a -20
BONUS: How can I move the decimal with multiplication?
Answers: 1) t > -1 2) m > -7 3) a < 114.4 BONUS: Multi/Divide by 10!
7.8 - The Metric System
7.8 - The Metric System
Conversion Practice Answers •1000 mg = 1 g •1 l = 1000 ml •160 cm = 1600 mm •14 km = 14000 m •109 g = 0.109 kg •250 m = .250 km •56 cm < 6 m •7 g > 698 mg
Metric Conversion Challenge Write the correct abbreviation for each metric unit. 1) Kilogram _____
4) Milliliter _____
7) Kilometer _____
2) Meter _____
5) Millimeter _____
8) Centimeter _____
3) Gram _____
6) Liter _____
9) Milligram _____
Try these conversions, using the ladder method. 10) 2000 mg = _______ g
13) 5 L = _______ mL
16) 16 cm = _______ mm
11) 104 km = _______ m
14) 198 g = _______ kg
17) 2500 m = _______ km
12) 480 cm = _____ m
15) 75 mL = _____ L
18) 65 g = _____ mg
Conversion Challenge ANSWERS
1) 2) 3) 4) 5) 6) 7) 8) 9)
kg m g mL mm L km cm mg
10) 2 g 11)104,000 m 12) 4.8 m 13) 5000 mL 14) 0.198 kg 15) 0.075 L 16) 160 mm 17) 2.5 km 18) 65,000 mg
Ladder Method
1 2 KILO 0.001 Units
3 HECTO 0.01 Units
DEKA 0.1 Units DECI 10 Unit Meters Liters Grams
How do you use the “ladder” method?
CENTI 100 Unit
MILLI 1000 Unit
4 km = _________ m
1st – Determine your starting point.
Starting Point
2nd – Count the “jumps” to your ending point.
How many jumps does it take?
3rd – Move the decimal the same number of jumps in the same direction.
Ending Point
4. __. __. __. = 4000 m 1
2
3
Conversion Practice
Try these conversions using the ladder method. 1000 mg = _______ g
1 L = _______ mL
160 cm = _______ mm
14 km = _______ m
109 g = _______ kg
250 m = _______ km
Compare using <, >, or =. 56 cm
6m
7g
698 mg
Compare using <, >, or =. 25) 63 cm
26) 536 cm
6m
53.6 dm
27) 5 g
28) 43 mg
508 mg
5g
29) 1,500 mL
30) 3.6 m
1.5 L
36 cm
Conversion Challenge 25. < 28. = 26. > 29. < 27. = 30. >
7-8 Using the Metric System
P 360 (4-30 EVEN)
Complete Rows 1-8 on KHAN by Monday, April 8th “1-Digit Addition” to “Equivalent Fractions 2”
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