Prerequisite Skills ReviewBefore Chapter 3

Finding Percents of Numbers

Finding Percents of Numbers

36% of 94.5

Finding Percents of Numbers

Finding Percents of Numbers

36% of 94.5

(0.36)(94.5) = 34.02

Finding Percents of Numbers

Find the percent of the number.

16% of 540

Finding Percents of Numbers

Find the percent of the number.

29% of 67.3

Finding Percents of Numbers

Find the percent of the number.

4% of 15

Checking Possible Solutions

Check whether the number 2 is a solution of the equation:

11747 yy

Checking Possible SolutionsCheck whether the number 2 is a solution of the equation:

111311141111487

11)2(7)2(4711747

yy

NO!!

Checking Possible Solutions

Check whether -3 is a solution of the equation:

1864 a

Checking Possible Solutions

Check whether 9 is a solution of the equation:

3542 x

Using the Distributive Property

Use the Distributive Property to simplify the expression.

)172(4 y

Using the Distributive Property

Use the Distributive Property to simplify the expression.

688)17)(4()2)(4(

)172(4

yyy

Using the Distributive Property

Use the Distributive Property to simplify the expression.

)12(8 y

Using the Distributive Property

Use the Distributive Property to simplify the expression.

)2)(6( x

Using the Distributive Property

Use the Distributive Property to simplify the expression.

)3)(452( x

Simplifying Like Terms

Find the terms of the expression.Then simplify by combining like terms.

)9.3(22.4 x

Simplifying Like Terms

Find the terms of the expression.Then simplify by combining like terms.

xx

xx

xx

21228.72.4

)]2()8.7[(2.4)])(2()9.3)(2[(2.4

)9.3)(2(2.4)9.3(22.4

Simplifying Like Terms

Find the terms of the expression.Then simplify by combining like terms.

ss 75.253

Simplifying Like Terms

Find the terms of the expression.Then simplify by combining like terms.

)449( xxx

Chapter 3Solving Linear Equations

3.1. Solving Equations Using Addition and Subtraction

You find $10 on the sidewalk and put it in your pocket. Later that day you empty your pocket and

find that you have $28.

How much did you have before you find the $10?

You could find the answer by using the model:

x + 10 = 28

or

28 - 10 = x

1. Open your Book to Page 133.2. Look at Example 1.

x – 5 = -13

3. Why is 5 instead of 13 added to both sides of the equation to solve for x?

What is a “solution step”?

Each time you apply a transformation to an equation, you are writing a solution step. Solution steps are written one

below the other with the equals signs aligned.

Example: Simplifying First

Solve )4(8 n

Example: Simplifying First

Solve

1212

48)4(8

nnnn

What is a “Linear Equation”?

In a linear equation the variable is raised to the first power and does not occur in a denominator, inside a square root symbol, or inside absolute value symbols.

Linear Equation Not a Linear Equation

62495

nnx

7|3|952

xx

What is a “Linear Equation”?

In Chapter 4, you will see that Linear Equations get their name from the fact that their graphs

are straight lines.

Translating Verbal StatementsMatch the real-life problem with an equation:

You owe $16 to your cousin. You paid x dollars back and you now owe $4. How much did you pay back?

x – 4 = 16 x = 16 + 4 16 – x = 4

Translating Verbal StatementsMatch the real-life problem with an equation:

x + 16 = 4 x = 16 + 4 16 – x = 4

The temperature was xo F. It rose 16o F and is now 4oF. What was the original temperature?

Translating Verbal StatementsMatch the real-life problem with an equation:

A telephone pole extends 4 feet below ground and 16 feet above ground. What is the total length x of the pole?

x – 4 = 16 x = 16 + 4 16 – x = 4

PRACTICE

Solve: x – 9 = -17

PRACTICE

Solve: x – 9 = -17x = -8

PRACTICE

Solve: – 11 = n – (-2)

PRACTICE

Solve: – 11 = n – (-2)n = -13

Practice

The normal high temperature in January in Bismarck, North Dakota, is 20oF and the normal low temperature is -2oF. How many degrees apart are the normal high and low temperatures?

Practice

The normal high temperature in January in Bismarck, North Dakota, is 20oF and the normal low temperature is -2oF. How many degrees apart are the normal high and low temperatures?

22oF

3.1. Closure Question

Describe in words how you would solve the equation x + 6 = -4 for x using inverse operations.

3.1. Closure Question

Describe in words how you would solve the equation x + 6 = -4 for x using inverse operations.

Subtract 6 from both sides of the equation to get x = -10.

Chapter 3Solving Linear Equations

3.2. Solving Equations Using Multiplication and Division

Dividing Each Side of an Equation

Solve 14 x

Dividing Each Side of an Equation

Solve 14 x

41

41

44

14

x

x

x

Example:

Solve 23 x

Multiply Each Side of an Equation

Solve 305

x

Multiply Each Side of an Equation

Solve 305

x

150

)5)(30(

305

x

x

x

Example:

Solve 259

x

Multiplying Each Side by a Reciprocal

Solve m3210

Multiplying Each Side by a Reciprocal

m

m

m

m

15230

32

23)10(

233210

Example:

Solve m8714

Properties of Equality

The transformations used to isolate the variable in Lessons 3.1 and 3.2 are based on rules of algebra called “properties of equality.”

Properties of Equality

Addition Property of Equality

If a = b, then a + c = b + c.

Properties of Equality

Subtraction Property of Equality

If a = b, then a - c = b - c.

Properties of Equality

Multiplication Property of Equality

If a = b, then ca = cb.

Properties of Equality

Division Property of Equality

If a = b and c ≠ 0, then

cb

ca