VocabularyVocabulary

Inequality: A mathematical sentence that compares the values of two expressions using an inequality symbol.

Solution of an inequality: any number that makes the inequality true.

Example: the solutions of the inequality x < 3, are all numbers that are less than 3.

Is each number a solution of x 5?

ALGEBRA 1 LESSON 3-1ALGEBRA 1 LESSON 3-1

>

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

a. –2 b. 10 c. 255

Inequalities and Their GraphsInequalities and Their Graphs

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ALGEBRA 1 LESSON 3-1ALGEBRA 1 LESSON 3-1

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.

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Tip:Always make sure the variable is on the left before you graph…..

Because……..

Your solutions……..

(are you ready???????)

Will always be……..

in the direction………

your inequality………

is pointing……

****This is why we always SWITCH and FLIP!!!

Graphing InequalitiesGraphing Inequalities

Since the solution of an inequality is not just one number, you can use a graph to indicate all of the solutions.

Inequality Graph x<3

m > -2

-1 > a*switch (variable and number) and flip (inequality) first* will explain on next slide

*The open dot shows that 3 is not a solution. Shade to the left of 3.

*The closed dot shows that -2 is a solution. Shade to the right of -2

*The closed dot shows that -1 is a solution. Shade to the left of -1.

a. Graph d < 3.

ALGEBRA 1 LESSON 3-1ALGEBRA 1 LESSON 3-1

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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Write an inequality for each graph.

ALGEBRA 1 LESSON 3-1ALGEBRA 1 LESSON 3-1

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.

12

12

ALGEBRA 1 LESSON 3-1ALGEBRA 1 LESSON 3-1

Define a variable and write an inequality for each situation.

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.>

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ALGEBRA 1 LESSON 3-1ALGEBRA 1 LESSON 3-1

Inequalities and Their GraphsInequalities and Their Graphs

pages 136–139  Exercises

2. no

4. yes

6. yes

8. yes

10. a. yes   b. no   c. yes

12. a. yes   b. no   c. no

14. a. no   b. no   c. yes

16. B

18. A

20.

22.

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24.

26.

ALGEBRA 1 LESSON 3-1ALGEBRA 1 LESSON 3-1

1. Is each number a solution of x > –1?

a. 3 b. –5

2. Is 2 a solution of 3x – 4 < 2?

3. Graph x > 4.

4. Write an inequality for the graph.  

5. Graph each inequality.

a. t is at most 2. b. w is at least 1.

yes no

no

p –2<

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Answers:Answers:

Check your answers and turn in please.

4. Yes

10(a). Yes

12(b). No

14(c). Yes

16. B

20. O

23. O

28. X ≤ 7

32. X < -1/2

34. a ≥ 16

-3

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