1-9 introduction to inequalities course 3 warm up warm up problem of the day problem of the day...

1-9 Introduction to Inequalities

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpSolve.

1. x + 6 = 132. 8n = 483. t 2 = 564. 6 =

x = 7

n = 6t = 58

z = 36z6


Course 3

Problem of the Day

Bill and Brad are taking Drivers education class. Bill drives with his instructor for one and a half hours three times a week. He needs a total of 27 hours. Brad drives two times a week, two hours each time. He needs 26 hours. Who will finish his hours first? Bill


Course 3

Learn to solve and graph inequalities.


Course 3

Vocabularyinequalityalgebraic inequalitysolution set


Course 3

An inequality compares two quantities and typically uses one of these symbols:

<<is less than

is greater than

is less than or equal to

is greater than or equal to


Course 3

Additional Example 1: Completing an Inequality

Compare. Write < or >.

A. 23 – 14 6

9 6>

B. 5(12) 70

60 70<


Course 3

Check It Out: Example 1

Compare. Write < or >.

A. 19 – 3 17

16 17<

B. 4(15) 50

60 50>


Course 3

An inequality that contains a variable is an algebraic inequality.

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

The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line.


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An open circle means that the corresponding value is not a solution. A solid circle means that the value is part of the solution set.

Helpful Hint!


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x < 5

4 < 5x = 2.1 2.1 < 5

x is less than 5Word

Phrase

Inequality

Sample Solutions

Solution Set 1 2 3 4 5 6 7

x = 4


Course 3

a > 0

7 > 0a = 25 25 > 0

a is greater than 0

a is more than 0Word

Phrase

Inequality

Sample Solutions

Solution Set–3 –2 –1 0 1 2 3

a = 7


Course 3

y 2

0 2y = 1.5 1.5 2

y is less than or equal to 2

y is at most 2Word

Phrase

Inequality

Sample Solutions

Solution Set–3 –2 –1 0 1 2 3

y = 0


Course 3

m 3

17 3m = 3 3 3

m is greater than or equal to 3

m is at least 3Word

Phrase

Inequality

Sample Solutions

Solution Set–1 0 1 2 3 4 5

m = 17


Course 3

Most inequalities can be solved the same way equations are solved.

Use inverse operations on both sides of the inequality to isolate the variable.

There are special rules when multiplying or dividing by a negative number, which you will learn in the next chapter.


Course 3

The inequality symbol opens to the side with the greater number.

2 < 10

Remember!


Course 3

Additional Example 2A: Solving and Graphing Inequalities

Solve and graph the inequality.

x + 2.5 8 –2.5 –2.5

x 5.5

1 2 3 4 5 6 7

Subtract 2.5 from both sides.

According to the graph, 5.4 is a solution, since 5.4 < 5.5, and 6 should not be solution because 6 > 5.5.


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Additional Example 2A Continued

Solve and graph the inequality.Check


Course 3

Substitute 5.4 for x.

7.9< 8 ?

So 5.4 is a solution.

x + 2.5 < 8 ?

5.4 + 2.5 < 8 ?

Check

Substitute 6 for x.

8.5< 8 ?

So 6 is not a solution.

x + 2.5 < 8 ?

6 + 2.5 < 8 ?

Additional Example 2B: Solving and Graphing Inequalities

Solve and graph the inequality.

w – 1 < 8

w < 9

–3 0 3 6 9 12 15

+ 1 + 1 Add 1 to both sides.


Course 3

Check It Out: Example 2

Solve and graph each inequality.

A. x + 2 3.5 –2 –2x 1.5

1 2 3 4 5 6 7

Subtract 2 from both sides.

B. 6u > 72

6 6

u > 12 3 6 9 12 15 18 21

6u > 72 Divide both sides by 6.


Course 3

Lesson Quiz

Use < or > to compare each inequality.

1. 13 5(2) 2. 14 – 2 11

Solve and graph each inequality.

3. k + 9 < 12

4. 3

5. A school bus can hold 64 passengers. Three classes would like to use the bus for a field trip. Each class has 21 students. Write and solve an inequality to determine whether all three classes will fit on the bus.

>

6 m

>

k< 3

m2

–5 –4–3–2–1 0 1 2 3 4 5

–4 –3–2–1 0 1 2 3 4 5 6

3(21) 64; 63 64; yes?


Course 3

1-9 introduction to inequalities course 3 warm up warm up problem of the day problem of the day...

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