Prerequisite Skills Review Before Chapter 3 Finding Percents

Prerequisite Skills Review Before Chapter 3

Finding Percents of Numbers 36% of 94. 5

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:

Checking Possible Solutions Check whether the number 2 is a solution of the equation: NO!!

Checking Possible Solutions Check whether -3 is a solution of the equation:

Checking Possible Solutions Check whether 9 is a solution of the equation:

Using the Distributive Property Use the Distributive Property to simplify the expression.

Simplifying Like Terms Find the terms of the expression. Then simplify by combining like terms.

Chapter 3 Solving 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

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

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 Statements Match 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 Statements Match the real-life problem with an equation: The temperature was xo F. It rose 16 o F and is now 4 o. F. What was the original temperature? x + 16 = 4 x = 16 + 4 16 – x = 4

Translating Verbal Statements Match 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 = -17 x = -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 20 o. F and the normal low temperature is -2 o. F. How many degrees apart are the normal high and low temperatures?

Practice The normal high temperature in January in Bismarck, North Dakota, is 20 o. F and the normal low temperature is -2 o. F. How many degrees apart are the normal high and low temperatures? 22 o. F

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 3 Solving Linear Equations 3. 2. Solving Equations Using Multiplication and Division

Dividing Each Side of an Equation Solve

Example: Solve

Multiply Each Side of an Equation Solve

Example: Solve

Multiplying Each Side by a Reciprocal Solve

Multiplying Each Side by a Reciprocal

Example: Solve

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. ”