Section 3-1 Inequalities and their GraphsSPI 22N: identify the graphical representation of the solution to a one variable inequality on a number line

Objectives:• Identify solutions of inequalities• Graph and write inequalities

VocabularySolution of an inequality:

• any number that makes the equation true.Example: For the inequality x > 3, all numbers that are less than 3 make the inequality true.

Remember the Signs of Inequality> Greater than< Less than= Equal to Less than and equal to Greater than and equal to

Is each number a solution of x 5?>

Yes, 5 5 is true. >No, –2 5 is not true. > Yes, 10 5 is true.>

a. –2 b. 10 c.255

Is each number a solution of 3 + 2x < 8?

a. –2 b. 3

3 + 2x < 8

–2 is a solution.

3 + 2(–2) < 8 Substitute for x.

3 – 4 < 8 Simplify.

–1 < 8 Compare.

3 + 2x < 8

3 is not a solution.

3 + 2(3) < 8 Substitute for x.

3 + 6 < 8 Simplify.

9 < 8 Compare.

Practice Understanding Inequalities

a. Graph d < 3. b. Graph –3 ≥ g.

The solutions of d < 3 are all the points to the left of 3.

The solutions of –3 g are –3 and all the points to the left of –3.

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An inequality may have more than one solution. Use the following symbols to graphically represent solutions to an inequality.

Closed dot on a number line shows solution includes value Open dot on a number line shows solution does not include value

Representing Inequalities on a Number Line

x < 2 Numbers less than 2 are graphed.

x > –2 Numbers greater than –2 are graphed.

x –3 Numbers less than or equal to –3 are graphed.

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>x Numbers greater than or equal to are graphed.

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Writing Inequalities from Number Lines

a. A speed that violates the law when the speed limit is 55 miles per hour.

b. A job that pays at least $500 a month.

Let v = an illegal speed.

The speed limit is 55, so v > 55.

Let p = pay per month.

The job pays $500 or more, so p 500.>

How would you graph the solutions to the above problems on a number line?

Write an Inequality for each Situation

Real World: Using Inequalities

Suppose your school plans a musical. The goal is to have ticket sales of at least $4000. Adult tickets are $5.oo and student tickets are $4.00. Let a represent the number of adult tickets and s represent the number of student tickets.

Write an inequality that represents the school’s goal.

5a + 4s 4000