Holt McDougal Algebra 1 Graphing and Writing Inequalities Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Holt McDougal Algebra 1

Graphing and Writing InequalitiesGraphing and Writing Inequalities

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt McDougal Algebra 1

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Warm UpCompare. Write <, >, or =. 1. –3 2 3.

2. 6.5 6.3 < >

> 4. 0.25 =

Tell whether the inequality x < 5 is true or false for the following values of x.

5. x = –10 T 6. x = 5 F

7. x = 4.99 T 8. x = T

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Identify solutions of inequalities with one variable.

Write and graph inequalities with one variable.

Objectives

Holt McDougal Algebra 1

Graphing and Writing Inequalities

inequalitysolution of an inequality

Vocabulary

Holt McDougal Algebra 1

Graphing and Writing Inequalities

An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs:

≤A ≤ B

A is less than or

equal to B.

<A < B

A is lessthan B.

>A > B

A is greaterthan B.

≥A ≥ B

A is greaterthan or

equal to B.

≠A ≠ B

A is notequal to B.

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

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Describe the solutions of 2p > 8 in words.

Check It Out! Example 1

Solution?

–6 8>?

–3–6

No 0 8>

?7.8 8

8 8

8.2 8 10 8

p2p

0 3.9 4 4.1 50 7.8 8 8.2 10

NoNo No Yes Yes

When the value of p is a number less than 4, the value of 2p is less than 8.

When the value of p is 4, the value of 2p is equal to 8

When the value of p is a number greater than 4, the value of 2p is greater than 8.

It appears that the solutions of 2p > 8 are all real numbers greater than 4.

>? >

?>? >

?2p > 8

?

Holt McDougal Algebra 1

Graphing and Writing Inequalities

An inequality like 3 + x < 9 has too many solutions to list. You can use a graph on a number line to show all the solutions.

The solutions are shaded and an arrow shows that the solutions continue past those shown on the graph. To show that an endpoint is a solution, draw a solid circle at the number. To show an endpoint is not a solution, draw an empty circle.

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Graph each inequality.Check It Out! Example 2

a. c > 2.5 Draw an empty circle at 2.5.

Shade in all the numbers greater than 2.5 and draw an arrow pointing to the right.

b. 22 – 4 ≥ w 22 – 4 ≥ w

4 – 4 ≥ w0 ≥ w

–4 –3 –2 –1 0 1 2 3 4 5 6

Draw a solid circle at 0.

Shade in all numbers less than 0 and draw an arrow pointing to the left.

c. m ≤ –3 Draw a solid circle at –3.

Shade in all numbers less than –3 and draw an arrow pointing to the left.

–4 –3 –2 –1 0 1 2 3 4 5 6

–4 –2 0 2 4 6 8 10 12 –6 –8

–3

2.5

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Example 3: Writing an Inequality from a Graph

Write the inequality shown by each graph.

Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2 means that 2 is not a solution, so use <.

x < 2

Use any variable. The arrow points to the right, so use either > or ≥. The solid circle at –0.5 means that –0.5 is a solution, so use ≥.

x ≥ –0.5

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Write the inequality shown by the graph.

Check It Out! Example 3

Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2.5 means that 2.5 is not a solution, so use so use <.

x < 2.5

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Reading Math

“No more than” means “less than or equal to.”

“At least” means “greater than or equal to”.

Holt McDougal Algebra 1

Graphing and Writing Inequalities

A store’s employees earn at least $8.50 per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.

Check It Out! Example 4

Let w represent an employee’s wages.

An employee earns at least $8.50

w ≥ 8.50

4 6 8 10 12−2 0 2 14 16 18

8.5w ≥ 8.5

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Lesson Quiz: Part I1. Describe the solutions of 7 < x + 4.

all real numbers greater than 3

2. Graph h ≥ –4.75

–5 –4.75 –4.5

Write the inequality shown by each graph.

3. x ≥ 3

4. x < –5.5

Holt McDougal Algebra 1

Graphing and Writing Inequalities

Lesson Quiz: Part II

5. A cell phone plan offers free minutes for no more than 250 minutes per month. Define a variable and write an inequality for the possible number of free minutes. Graph the solution.

0 ≤ m ≤ 250

0 250

Let m = number of minutes