Warm Up Sept. 20Sit in your usual seat with your tracking sheet out.

Answer the following questions.

1. How did you feel about the test yesterday? What parts were easy or hard?

2. -4(x + 2) + 8 = 2(x – 1) – 7x + 15

3. -x + 4 = x + 6

4. Twelve is added to the product of a number and 10. The result is 8. Find the number.

Who would like a textbook?

One-Step Inequalities

Inequalities represent a set of numbers.

What are some real life situations that inequalities could represent?• The weather man says it is going to be

at least 70 degrees today.

• You refuse to pay more than $40 for a pair of shoes you want.

• In order to ride the Intimidator at Carowinds, you must be at least 56 inches tall.

What do we use to represent inequalities? > < > <

How would this look on a graph?

Graphing An Inequality

Read the inequality out loud to yourself. Decide if the variable is greater than or less than the number.

If the variable is greater than shade to the right

If the variable is less than shade to the left

Another way to think about it:As long as the variable is in front of the inequality, shade in the direction the arrow is pointing.

Examples:

x < 5 x > 11

Graphing an Inequality

Graphing an Inequality

You Try

x > -3 x < 0

How about these two?

-5 < x 10 > 5

A solution of an inequality is any number that makes the inequality true.

Identifying Solutions by Evaluating

Examples

Is the number a solution of 2x + 1 > -3?

1. -3 2. -1

Identifying Solutions by Evaluating

You Try

Is the number a solution of 13 – 7y ≤ 6?

1. -1 2. 0

3. 1 4. 3

Solve by Addition and Subtraction• Solve for n and check the solution.

Example

1.

Set-Builder Notation:

Read as _____________________________________.

74 n

Solve by Addition and Subtraction

Example

2. x + 6 < -2

Set-Builder Notation:

Read as _____________________________________.

You Try • Solve and graph.

914 .4

6512 .3

y

x

Solve by Multiplication & Division• When you divide or multiply by a negative

number, you must flip your inequality sign.

Examples:

1. 2. 24

5

25

8 y

x

You Try

h-

w

1040 .4

639

7 .3

Write and Solve an InequalityExample

1. A number decreased by 8 is at most 14.

Write and Solve an Inequality (cont.)You Try

2. Seven times a number is greater than six times that number minus two.

3. Four times a number is no more than -108.

4. One fifth of a number is at least 3.

Real World Examples1. Alicia wants to buy season passes to two

theme parks. If one season pass costs $54.99 and Alicia has $100 to spend on passes, the second season pass must cost no more than what amount?

Real World Examples2. Pet Supplies Superstore makes a profit of

$5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?

HomeworkWorksheet on the back of your

notes for today.

Exit Ticket1. Given the inequality 2r + 5 < 15, is 3 a solution? Is

10 a solution? Why or why not?

2. Graph the following inequality: x < 5.

3. A number divided by 2 is at least 30. Write an inequality to represent this situation.

4. A Girl Scout Troop needs to raise $930 dollars to go on their annual camping trip. If they sell boxes of cookies for $3.50 each, how many boxes do they need to sell in order to have at least enough to go on their trip?