Solving Equations and Inequalities · Solving Equations & Inequalities 7.2 -Solving Two-Step...

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 ���� in.

1. c – 19 = 17

2. -3n + 8 = -7

3. 2 + 4m = 1

4. 3 = n - 3

4

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. 20 = 6x + 82. -10 – k = -363. 2y – 7 = 154. 15- 4g = - 335. 2.1 = 0.8 – z

6. -17 + �

�= 3

7.���

� 36

8. - 49 = �

+ 11

Answers:

1. x = 22. k = 263. y = 114. g = 125. z = - 1.3 6. t = 1007. k = - 1268. 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

Oh, number Pi

Oh, number Pi

Your digits are unending,

Oh, number Pi

Oh, number Pi

No pattern are you sending.

You're three point one four

one five nine,

And even more if we had time,

Oh, number Pi

Oh, number Pi

For circle lengths unbending.

� Notes:

Sing O Number Pi: (to the tune of "Oh Christmas Tree")

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 the circumference?

Answers:1) a = -52) b = -53) y = 44) m = 15) 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)

Answers1)a= 22)w = 33)t = -74)All 5)r = 46)Null7)m = - ½

HINT : “Null” means NO SOLUTION and it is NEVER true!

“All” means ALL NUMBERS are possible to make it true!

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

� Warm-Up: Please solve each equation

1. 5a – 18 = 3a

2. -3b + 13 = -b – 3

3. 4(2x – 1) – 3 = 5(x – 5)

4. 7(y – 3) – 2 = 3(2y – 5) + 4

5.4/7m + 5 = 2/7m – 3

Answers:

1) a = 92) b = 83) x = -64) y = 125) m = -28

7-6 Solving Multi-Step Inequalities

� NOTES:

7-6 Solving Multi-Step Inequalities

� NOTES:

7-6 Solving Multi-Step Inequalities

� NOTES:

Solve b – 8 ≥ 3b – 8 and check the solution.

Graph the solution on a number line.

b – 8 ≥ 3b – 8

+ 8 + 8

b ≥ 3b

– 3b – 3b

–2b ≤≤≤≤ 0

-2 -2

b ≤ ≤ ≤ ≤ 0

Rule: If each side of an inequality is multiplied or divided by a negative number, the order symbol of the inequality must be reversed.

1. Add 8 to each side.2. Subtract 3b from each side.3. Divide each side by –2

4. And change ≥≥≥≥ to ≤≤≤≤.

Solve 5m - 8 > 12

+ 8 + 8

5m > 20

5 5

m > 4

5(4) – 8 = 12

1. Draw “the river”

2. Add 8 to both sides

3. Simplify

4. Divide both sides by 5

5. Simplify

6. Check your answer

7. Graph the solution

o4 53

Solve 12 - 3a > 18- 12 - 12

-3a > 6

-3 -3

a < -2

12 - 3(-2) = 18

1. Draw “the river”

2. Subtract 12 from both sides

3. Simplify

4. Divide both sides by -3

5. Simplify (Switch the inequality!)

6. Check your answer

7. Graph the solution

o-2 -1-3

Which graph shows the solution to:2x - 10 ≥ 4?

1. .

2.

3.

4.

Answer NowAnswer Now

Solve 5m - 4 < 2m + 11

- 2m -2m

3m - 4 < 11

+ 4 + 4

3m < 15

3 3

m < 5

5(5) – 4 = 2(5) + 11

1. Draw “the river”

2. Subtract 2m from both sides

3. Simplify

4. Add 4 to both sides

5. Simplify

6. Divide both sides by 3

7. Simplify

8. Check your answer

9. Graph the solution

o5 64

Solve 2r - 18 ≤ 5r + 3-2r -2r

-18 ≤ 3r + 3

- 3 - 3

-21 ≤ 3r

3 3

-7 ≤ r or r ≥ -7

2(-7) – 18 = 5(-7) +3

1. Draw “the river”

2. Subtract 2r from both sides

3. Simplify

4. Subtract 3 from both sides

5. Simplify

6. Divide both sides by 3

7. Simplify

8. Check your answer

9. Graph the solution

●-7 -6-8

6) Solve -2x + 6 ≥ 3x - 4

1. x ≥ -2

2. x ≤ -2

3. x ≥ 2

4. x ≤ 2

Answer NowAnswer Now

Solve 26p - 20 > 14p + 64-14p -14p

12p – 20 > 64

+ 20 + 20

12p > 84

12 12

p > 7

26(7) – 20 = 14(7) + 64

1. Draw “the river”

2. Subtract 14p from both sides

3. Simplify

4. Add 20 to both sides

5. Simplify

6. Divide both sides by 12

7. Simplify

8. Check your answer

9. Graph the solution

o7 86

What are the values of x if 3(x + 4) - 5(x - 1) < 5?

1. x < -6

2. x > -6

3. x < 6

4. x > 6

Answer NowAnswer 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. 21 - 4t < 25

2. 18 + 6m > -24

3. - 5.72 < a

-20

BONUS: How can I move the decimal

with multiplication?

Answers:

1) t > -12) m > -73) a < 114.4

BONUS:Multi/Divide by 10!

7.8 - The Metric System

7.8 - The Metric System

•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

Conversion Practice Answers

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

Metric Conversion Challenge

1) kg 2) m 3) g 4) mL5) mm 6) L7) km 8) cm 9) mg

10) 2 g 11)104,000 m 12) 4.8 m 13) 5000 mL14) 0.198 kg 15) 0.075 L 16) 160 mm 17) 2.5 km 18) 65,000 mg

Conversion Challenge ANSWERS

KILO0.001Units

HECTO0.01Units

DEKA0.1

UnitsDECI

10Unit

CENTI100Unit

MILLI1000Unit

MetersLitersGrams

Ladder Method

How do you use the “ladder” method?

1st – Determine your starting point.

2nd – Count the “jumps” to your ending point.

3rd – Move the decimal the same number of jumps in the same direction.

4 km = _________ m

1

23

How many jumps does it take?

Starting Point Ending Point

4.1

__.2

__.3

__. = 4000 m

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

Conversion Practice

Compare using <, >, or =.

56 cm 6 m 7 g 698 mg

Compare using <, >, or =.

25) 63 cm 6 m 27) 5 g 508 mg 29) 1,500 mL 1.5 L

26) 536 cm 53.6 dm 28) 43 mg 5 g 30) 3.6 m 36 cm

25. < 26. > 27. =

28. = 29. < 30. >

Conversion Challenge

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”

"March Math-ness" Extra Credit Game

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