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Day 1. Lesson 8.1 Solving Equations , ,

What is an equation? A statement that has _____ mathematical expressions, and they have the _________ value.

Ex. 1.

Miller High School Mathematics

Note: In 1. x is the ___________________2. 3 is the ___________________3. 1 & 10 are __________________

NAME: _________________________________

DATE: __________________________

BLOCK: ___________

TEACHER: ___________________________

MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT

MATHEMATICS 9CHAPTERS 8&9

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2.

How do we solve for x to show that both mathematical expressions equal?There are three ways:

1. Balance Strategy: a)

b)2. Diagram:

a)

b)

3. Solving Algebraically:You can solve equations algebraically by applying the ____________(or inverse) operation. Examples of opposite operations are:

a) When you have an addition, you _______________.b) When you have a subtraction, you _______________.c) When you have a multiplication, you _______________.d) When you have a division, you __________________.

Ex. Solve each equationa) b) c) d)


0 1 2 3 654 7 1098

0 1 2 3 654 7 1098

Now, let’s apply this concept to solving equations with fractions and decimals.

1. It is important to check your answer by substituting into the formula.

Left side = 3x Right side =

2. 3. 4.

5. 6. 7.

8. 9. 10.

Note: Change the mixed fractions to the improper first. Solving Word Problems

a) Jacko’s Warehouse is selling jackets at 30% off the regular price? If the sale price is $34.99, what is the regular price of the jackets?


b) The density of an object is determined by the formula , where m is the mass,

in grams, and v is the volume, in litres. What volume does the object occupy if an 8.58-g object has a density of 3.3 g/L?

c) Spencer spends 30% of his net income on rent and 30% of his net income on food. If she spends a total of $1225 per month on rent and food, what is his net monthly income?

Day 2. Lesson 8.2 Solving Equations ,

Recall:To solve equations algebraically, apply the ____________(or inverse) operation. Examples of opposite operations are:

e) When you have a multiplication, you _______________.


f) When you have a division, you __________________.g) When you have an addition, you _______________.h) When you have a subtraction, you _______________.

If we want to isolate the variable in a two-step equation, ______________ or ____________ first, and then multiply or divide.

Ex. 0.4w – 1.5 =0.3

To solve two-step equations involving fractions, you may prefer to rewrite the equation and work with _______________ than to perform fraction operations. For example:

Ex.

We can also use diagrams to help us solve equations:

Ex.

Solve each equation:a. b. c.


To work with integers, ____________ all terms by a common multiple of the ______________. For the denominators 5, 2, and 10, a common multiple is _______.

0

d. e. f.

Example 3: Solve each problem.

a) Enrico delivers pizza for Pepe’s Pepperoni Pizza. He earns $15.60 plus $0.60 per pizza delivered. How many pizzas does he need to deliver to earn a total of $30?

b) The cost of a banquet at Nick’s Catering is $215 plus $27.50 per person. If the total cost of a banquet was $2827.50, how many people were invited?

c) An isosceles triangle with a perimeter of 50.6 cm has one short side and two equal longer sides. The short side is 10.8 cm. Write and solve an equation to determine the length of one longer side?

Day 3. Lesson 8.3: Solving Equations (Part 3)

To isolate the variable in an equation of the form a(x+b) = c, you can use the ___________________ property first.

4(x – 0.6) =-3.2


Observe:

To solve equations involving grouping symbols and fractions, you can rewrite the equation and work with _______________ instead of performing fraction operations. For example:

Example 1: Solve each equation

a) 2(x – 4) = 12 b) 3(x + 0.5) = –2.1 c) 1.2(x + 1.3) = 2.4

d) e) f)

Example 3: Solve each problem.

a) The perimeter of a square is 49.2 cm. The side length of the square is represented by the expression (x + 4.1) cm. What is the value of x?


To work with fractions, multiply all terms by a _____________ multiple of the denominators. For the denominators 2 and 4 a common multiple is ____.

b) Two equilateral triangles differ in their side lengths by 1.03 m. The perimeter of the larger triangle is 9.24 m. Determine the side length of the smaller triangle by representing the situation with an equation of the form a(x+b)=c and solving the equation.

c) On a typical day in October in Churchill, Manitoba, the daily average temperature is -1.5 deg C? The high temperature is 1.3 deg C. Calculate the low temperature.

Day 4. Lesson 8.4 Solving Equations

To solve equations with variables on both sides by applying the techniques learned in earlier sections.

Steps: 1. Use the ________________ property to expand.2. Isolate the ________________ to one side of the equation.3. Solve for ______.


(a) 3(0.5x + 1.3) =2(0.4x – 0.85) (b) 6(x – 1.5)=5(2x+1.8)

Practice: Solve each equation

a) 5(2x + 1.2) = 4(x – 1.5) b) 1.3x + 64.2 = 2.7x + 12.82

c) 1.2x – 17 = 8 + 0.7x d)

e) 0.3(2x – 1) – 2.3 = 0.04(x + 5) f)

Solve each problem.a) In a jar of coins, there are 20 more nickels than quarters. The value of nickels

equals the value of the quarters. How many quarters are in the jar?


b) Nick has $30.68 saved and earns $11.25/week. Alice has $24.18 saved and earns $13.75/week. In how many weeks will they have the same amount of money?

c) Jack rode his bike to school at 11.2 km/hr. He returned home using the same route at 8.3 km/hr. Jack took at total of 45 min to ride to school and back. Express you answers to the nearest hundredth (to two decimal places).

i) How many minutes did Jack take to ride to school? ii) How far is it from Jack’s house to school?

Day 6. Lesson 9.1 Representing Inequalities

A _____________ _____________ compares linear expressions that may not be equal. x≥-3 means that x is greater than or equal to -3

Inequality can be expressed ____________ , ____________ , and algebraically.

Inequality Meaning

a>b a is greater than b


a<b a is less than ba≥b a is greater than or equal to ba b a is less than or equal to ba=b a is not equal to b

Ex. 1 During the flu season of 2009, children over the age of 6 months are encouraged to receive their H1N1 vaccine.

Graphically: | | | | | | | 0 3 6 9 12 15 18

Algebraically: Let a = children over the age of 6 months

Verbally: Children ________________________ should get their H1N1 vaccine.

______________ _____________ separates the values less than from the values greater than a specified value. ______________ _____________ may or may not be a possible value.

Ex. 2

| | | | | | | | | | | | | | | 0 1 0 1

a ¾ a ½ Represent the following algebraically and verbally:

| | | | | | | | | | | | | | | -4 -3 -2 5 6

Algebraically: _________________________ ____________________________________

Verbally: _____________________________ ____________________________________

Ex. 3 a) Express the inequality shown on the number line verbally and algebraically.

| | | | | | | | | | | | | | -20 -15 -10

Verbally: ____________________________________________________________

b) Express the inequality shown on the number line algebraically.


An Open circle shows that the boundary point is not included in this solution

A Closed circle shows that the boundary point is included in this solution

a) b)

| | | | | | | | | | | | | | __________________ 2 3

c) Express the inequality x -4/7 verbally ____________________________

d) Express the inequality 35< n graphically

Ex. 4 Represent Double InequalitiesRepresent the situation described in the newspaper headline with an inequality. Show it verbally, graphically, and algebraically.

Verbally: ____________________________________________________________

Algebraically: _______________________________________

Graphically:

Day 7. Chapter 9.2 Solving Single-Step Inequalities4 The solution to an inequality is the value or values that makes the inequality true.

Ex. Solve for 5x > 10:

A specific solution is any value greater than 2. For example, 2.1, 3, 22.84. The set of all solutions is x >2. Represent the following algebraically and verbally:


Average Daily Water Use From 327L to 343L Per

Person

| | | | | | | | 1 2 3

You can solve an inequality involving addition, subtraction, multiplication and division by isolating the variable. a) x + 5 ≤ 12 b) 4x ≤ –16

c) – ≥ 3 d) -2x + 6 ≤ 14

To verify the solution to an inequality, substitute possible values into the inequality:

1. Solve for the inequality – 8x< 24 2. Substitute the value for the boundary point to check if both sides are equal:

2. Substitute a value greater than the boundary point – 3 to check that the inequality symbol is correct.

4. A balloon company guarantees that at least 18 of the balloons in each package are red. Fifteen percent of the balloons are red. What is the number of balloons in a package?a) Write an inequality to model the situation.


When multiplying or dividing by a negative, you must _______________ the sign.

b) Solve and verify the inequality.

c) Represent your answer verbally and graphically.

5. a) Write and solve an equation to determine the values of x that give the rectangle shown an area of no more than 25 square units.

b) Are there values of x that would not be possible for the length of the rectangle? Explain.

Day 8. Lesson 9.3 Solving Multi-Step Inequalities

There are two ways to solve an equation involving multiple steps.

Ex. Solve , and verify the solution

Method 1 Method 2 Use the _____________ Property _______________ first


Verify the solution: Substitute a value greater than _____, Substitute the boundary point ____. such as 0.

Practice 1:

a) b)

c)


Practice 2:

Your parents are celebrating their 25th wedding anniversary. They have compared the rates at two banquet halls. Fancy Feast charges $200 for the hall plus $30 per person. Beautiful Banquet charges $400 for the hall plus $20 per person.

a) Write an inequality to represent the number of people who could attend the celebration at Fancy Feast with a cost of no more than $2000.

b) How many people need to attend to make Beautiful Banquet more cost efficient? Show your work.

Chapter 8-9 Assignment List

Chapters 8 & 9: Linear Equations & InequalitiesDay Section & Topic Basic Typical Enriched


1 8.1 Solve One-Step Equations

p301 #1, 4-6, 8, 10, 12, ML

p301 #1, 4-6, 8, 11-12, 14, 17, 19, 23, ML

p301 #1, 20-21, 23-29

2 8.2 Solve Two-Step Equations

p310 #1-3, 5-7, (9-15 o.n.), ML

p310 #1-3, 5-7, (9-15 o.n.), 16, 19, ML

p310 #1-3, 19-20, 23, 26-32

3 8.3 Solve Equations with Brackets

p318 #1, 4-6, (8-14 e.n.), 15, 17, ML

p318 #1, 4-6, (8-14 e.n.), 15, 17, 20, 22, ML

p318 #1, 4, 10, 20, 23-28

4 8.4 Equations with Variables on Both Sides

p326 #1-6, 8, 10, 14-15, ML

p326 #1-6, 8, 10, 14-15, 18, 25, ML

p326 #1-3, 16, 18, 22-24, 26-30

5 Ch 8 Quiz and Review p330 #1-20, (extra: p332 #1-14)

p330 #1-20, (extra: p332 #1-14)

p330 #1-20, (extra: p332 #1-14)

6 9.1 Representing Inequalities p346 #1-3, 5-7, 9, 10b, 11, 13, 15, 17, ML

p346 #1-3, 5-7, 9, 10b, 11, 16, 19, 21, ML

p346 #2-4, 8, 10, 13, 23-25, ML

7 9.2 Solve One-Step Inequalities

p356 #1-4, 5ad, 6ab, 7ad, 8-9, 12, 14, 16a, 17

p356 #1-4, 5ad, 6ab, 7ad, 8-9, 12, 14, 16-18

p356 #1-4, 5cd, 6bc, 13, 17, 19-25

8 9.3 Solve Multi-Step Inequalities p365 #1-3, 6, 8, 11 p365 #1-3, 6, 8,

10-14p365 #2, 7-8, 11, 13-14, 16-18, 20

9 Ch 9 Quiz and Review P368 #1-20 (extra: p370 #1-15)

P368 #1-20 (extra: p370 #1-15)

P368 #1-20 (extra: p370 #1-15)

Test Day: _______________________________________


lesson 3 - wikispaces8... · web viewlesson 9.3 solving multi-step inequalities there are two ways...

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