# Module 2 Unit 3 Notes

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PROBLEM OF THE WEEK!
November 30, 2012

Notes Module 2 Unit 3 Day 11-G, A: Equations and Solutions
Equation- two expressions set equal with an equal sign
Equation: x + 9 = 22           Expression: x + 9

Solution- the value for a variable that makes an equation true

Example 1: Determine whether the given value of the variable is a solution.

a)    18 = s - 7; s = 11                          b)   w + 17 = 23; w = 6

Example 2:
Tyler wants to buy a new skateboard. He has \$57, which is \$38 less than he needs. Does the
skateboard cost \$90 or \$95?

Example 3:
`
Determine whether the given value of the variable is a solution.

60 ÷ c = 6; c = 10

Example 4:    Use mental math to solve each equation.

a)   t-3=7                              b)
h
= 2.2
4

c)   4y = 20                            d)    n + 6 = 16.1
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Notes Module 2 Unit 3 Day 12-G: Solving Addition Equations
Inverse Operations- operations that undo another operation

Inverse operation of SUBTRACTION

Properties of Equality:
Subtraction Property of Equality
If you subtract the same amount to both sides of an equation, the two sides remain equal

Ex:   5+2=7

Solve and check each equation.

Examples:
x + 4 = 38                                      81 = 17 + y

w + 4.3 = 9.1                                    14.7 = 5 + f

Example:
When a kitten was brought home it weighed 15 ounces. After two years, the
kitten had grown into a cat weighing 120 ounces. How many ounces did the cat gain?
November 30, 2012

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November 30, 2012

Notes Module 2 Unit 3 Day 13-G: Solving Subtraction Equations
Inverse Operations- operations that undo another operation

Inverse operation of SUBTRACTION

Properties of Equality:
If you add the same amount to both sides of an equation, the two sides remain equal
Ex: 5 - 2 = 3

Solve and check each equation.
Examples:
c - 12 = 43                                   n - 53 = 28

40 = x - 11                                  7.9 = n - 0.35

Use order of operations to solve these expressions before you start your homework.

1.    24 ÷ 4 - 2 x 3                                2.    24 ÷ 3 - 2 x 4

3.    24 ÷ (3 - 2) x 4                              4.    (24 ÷ 3 - 2) x 4
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Notes Module 2 Unit 3 Day 14-G: Solving Multiplication Equations
Inverse Operations- operations that undo another operation (opposite)

Inverse operation of SUBTRACTION

Inverse operation of MULTIPLICATION

Inverse operation of DIVISION

Properties of Equality:
Division Property of Equality
If you divide each side of the equation by the same nonzero number, the two sides remain equal

Ex:   4 x 9 = 36

Solve and check each equation.
Examples:
3x = 12                                        68 = 4w

0.8p = 32                                      12m = 132

Example:
The area of a rectangle is 36 square inches. Its length is 9 inches. What is its width?
Recall that the area of a rectangle is the formula: A = lw
November 30, 2012

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Notes Module 2 Unit 3 Day 15-G: Solving Division Equations
Inverse Operations- operations that undo another operation (opposite)

Inverse operation of SUBTRACTION

Inverse operation of MULTIPLICATION

Inverse operation of DIVISION

Properties of Equality:
Multiplication Property of Equality
If you multiply each side of the equation by the same nonzero number, the two sides
remain equal
10
Ex:      =2
5

Solve and check each equation.
Examples:
y                                                       z
= 4                                      12 =
5                                                       4

y ÷ 43 = 1,204                                  w ÷ 1.5 = 10

Example:
Pressure is the amount of force exerted on an area. Pressure can be measured in
pounds per square inch, or psi. The pressure at the surface of the water is half the
pressure at 30 ft underwater.

Pressure at 30 ft underwater
Pressure at surface=
2

The pressure at the surface is 15 psi. What is the water pressure at 30 ft underwater?
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3-6 Guided Problem Solving Notes

Example 1:
You buy several posters. The total cost is \$18.95. You have \$7.05 left after you
pay. Write and solve an equation to find how much money you had before this purchase.

Example 2:
Jim has saved \$78. This is \$23 less than his sister has saved. Write and solve
an equation to find how much his sister has saved.

Example 3:
An elephant's height is about 5.5 times the length of her hind footprint. Use an
equation to fine the approximate height of an elephant whose hind footprint is 1.5 feet
long.

Example 4:
Angela makes 1.75 times the amount of money that Janet makes. If Janet makes
\$38,200, how much does Angela make? Write and solve an equation.
November 30, 2012

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Notes Module 2 Unit 3 Day 17: Dependent and Independent Variables
Variable- letters in algebra in which numbers are substituted in for

Independent Variable- a variable that stands alone…it is NOT affected by any other factors
Ex: Someone’s age is an independent variable because other factors (such as what they eat, what they
wear to school, etc) are not going to change how old someone is

Dependent Variable- a variable that changes depending on other factors
Ex: Test scores are a dependent variable because it could change depending on other factors (such
as how much you studied, how much sleep you got, etc)

Independent           Dependent
Label the dependent and independent variables:
Cause                Effect
y = 3x + 6
Input                Output
Before                After
What you do          What happens

Example 1: Identify the independent variable and the dependent variable.
a)    x = 5y + 10                        b)     6z + 12 = w

c)    3c - 15 = b

When you graph an equation, the independent variable should be on the x-axis and the dependent
variable should be on the y-axis.

Example 2: Identify which is the independent variable and which is the dependent variable.
a)  The number of days since your last hair cut and the length of your hair.

Dependent variable:                      Independent variable:

b)      The height of an oak tree and the number of years that have passed since the tree was planted.

Dependent variable:                      Independent variable:

c)      The miles traveled and the hours traveled at a constant speed.

Dependent variable:                      Independent variable:

d)      The number of points scored in a basketball game and the number of games played in a basketball
season.

Dependent variable:                      Independent variable:

Let’s practice graphing dependent and independent variables. Choose one of the above examples to graph.
November 30, 2012

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Notes Module 2 Unit 3 Day 19-G, A: Two-Step Equations
Two-Step Equations- an equation that contains two operations

Steps:
2.    Undo multiplication/division

Solve and check each equation.

3x + 2 = 14                                  2y + 3 = 11

5x + 3 = 18                                  3x - 4 = 23

7x - 11 = 38
November 30, 2012

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Notes Module 2 Unit 3 Day 20-G, A: Two-Step Equations

Solve and check each equation.

x
- 4 = 10                   +x = 9
5
9                            4

x                                    1
+ 8 = 13                  -x= 1
4                            4  4    8

x
+ 0.6 = 3.4
2
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Notes Module 2 Unit 3 Day 21-G, A: Writing and Solving Two-Step
Equations
Example 1: Define a variable and write an algebraic equation for each phrase.
a)    Three less than four times a number is twenty-five.

b)   Ten less than the quotient of a number and three is eight.

c)   One more than five times a number is forty-one.

d)   The product of eight and a number minus three is ninety-three.

e)   Twelve more than the quotient of a number and nine is twenty.

Example 2:
A fitness club advertises a special for new members. Each month of membership is \$19, with an
initial enrollment fee of \$75. Write an expression for the total cost. Then evaluate your expression.

Example 3:
Three neighbors host a party. Each neighbor buys a watermelon for \$8. They split the cost of
paper goods, p, equally. If each neighbor spends \$20, what is the total cost of the paper goods?
p
Solve the equation        + 8 = 20.
3

Example 4:
You order a backpack for \$34 and pens for \$2 each. You spend \$46, excluding the shipping cost
and tax. How many pens do you order? Let p represent the number of pens. Solve 2p + 34 = 46.

Example 5:
You save \$26 each week to buy a digital camera that costs \$260. You have already saved \$182.
In how many weeks will you save \$260? Let w represent the number of weeks to write and solve the
equation.

Example 6:
You and a friend split the cost of a moped rental. Your friend pays the bill. You owe your friend
only \$12, because your friend owed you \$9 from yesterday. How much was the total bill?

a)    Let m represent the cost of the moped rental. Write a two-step equation to represent the situation.

b)    Solve the equation.
November 30, 2012

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November 30, 2012

Notes Module 2 Unit 3 Day 22-S, G, A: Two-Step Equations

Example 1:
Your bicycle needs to be fixed. A mechanic charges \$40 for each hour of labor, and the new parts
cost \$35. The total cost of fixing the bicycle is \$95. How long did it take the mechanic to fix the
bicycle?

Cost of new parts + cost of labor per hour x number of hours of labor = total cost

Example 2:
You have \$15 to spend at the arcade. If you plan to spend \$3 on snacks, and games cost \$2 each,
how many games can you play?

Example 3:
Solomon decided to make posters for the student council election. He bought markers that cost
\$.79 each and a poster board that cost \$1.25. The total cost was \$7.57. Write and solve an equation to
find the number of markers that Solomon bought.

Example 4:
A skating rink rents skates at \$3.95 for the first hour plus \$1.25 for each additional hour. When
you returned your skates, you paid \$7.70. How many additional hours did you keep the skates?
November 30, 2012

Notes Module 2 Unit 3 Day 24: Transforming Equations
Use the simple interest formula: I = prt

Example 1:
Your bank account has an annual interest rate of 5.7%. How much should you invest in order to earn
\$100 in interest each year?

Example 2:
Find the interest rate that yields \$120 interest each year on \$2,000.
November 30, 2012

Welcome to Class!
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PROBLEM OF THE WEEK!
November 30, 2012

Welcome to Class!

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PROBLEM OF THE WEEK!
November 30, 2012

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Turn in any missing work

PROBLEM OF THE WEEK!

GOOD LUCK
November 30, 2012

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