Holt Algebra 1

3-1 Graphing and Writing Inequalities3-1 Graphing and Writing Inequalities

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

3-1 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 Algebra 1

3-1 Graphing and Writing Inequalities

Identify solutions of inequalities with one variable.

Write and graph inequalities with one variable.

Objectives

Holt Algebra 1

3-1 Graphing and Writing Inequalities

inequalitysolution of an inequality

Vocabulary

Holt Algebra 1

3-1 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 that makes the inequality true.

Holt Algebra 1

3-1 Graphing and Writing Inequalities

Example 1: Identifying Solutions of Inequalities

Describe the solutions of x – 6 ≥ 4 in words.

When the value of x is a number less than 10, the value of x – 6 is less than 4.

When the value of x is 10, the value of x – 6 is equal to 4.

When the value of x is a number greater than 10, the value of x – 6 is greater than 4.

It appears that the solutions of x – 6 ≥ 4 are all real numbers greater than or equal to 10.

Solution?

–9 4≥ ?

–3–9

No–6 4≥

?3.9 4 ≥

?4 4≥

?4.1 4≥

?6 4≥

?

x

x – 6

x – 6 ≥ 4

0 9.9 10 10.1 12–6 3.9 4 4.1 6

NoNo Yes Yes Yes

?

Holt Algebra 1

3-1 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 Algebra 1

3-1 Graphing and Writing Inequalities

Add to Notes: =

=

=

=><

≤≥

In Textbook:

Holt Algebra 1

3-1 Graphing and Writing Inequalities

Example 2: Graphing Inequalities

Graph each inequality.

A. m ≥

0 1– 2 3 3

Draw a solid circle at .

Shade all the numbers

greater than and draw an

arrow pointing to the right.B. t < 5(–1 + 3)

t < 5(–1 + 3)

t < 5(2)

t < 10

–4 –2 0 2 4 6 8 10 12 –6 –8

Simplify.

Draw an empty circle at 10.Shade all the numbers less than 10 and draw an arrow pointing to the left.

Holt Algebra 1

3-1 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 Algebra 1

3-1 Graphing and Writing Inequalities

Reading Math

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

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

“No more than” = ≤

= ≥

Add to Notes:

“At least”

Holt Algebra 1

3-1 Graphing and Writing Inequalities

Example 4: ApplicationRay’s dad told him not to turn on the air conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions.Let t represent the temperatures at which Ray can turn on the air conditioner.

75 80 85 9070

Turn on the AC when temperature is at least 85°F

t ≥ 85

Draw a solid circle at 85. Shade all numbers greater than 85 and draw an arrow pointing to the right.

t 85

Holt Algebra 1

3-1 Graphing and Writing Inequalities

L3-1 NOTES

“No more than” = ≤

= ≥“At least”

=

=

=

=><

≤≥

An inequality is a statement that two quantities are not equal.

Graphing inequalities:

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

Holt Algebra 1

3-1 Graphing and Writing Inequalities

Assignment

• L3-1 pg 171 #18-57x3, #72-81x3

Holt Algebra 1

3-1 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 Algebra 1

3-1 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