6th Grade Math Textbook, Fundamentals

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Lesson 3-2 for exercise sets.

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Find the solution set for each inequality. Then graph each on a number line.

1.x 9 2.x 2 3.x 0 4.x 

11

5.Discuss and Write Explain when you need to use a circle and when you need to use

a dot to graph solution sets of inequalities. Give examples to justify your answer.

Often the solution set is not limited to whole numbers. It may include other number

types such as integers, fractions, and decimals. To graph this type of solution set on a

number line, a line segment or a ray is used instead of separate dots. This shows that

all the numbers betweenwhole numbers are included in the solution set.

Graph:x  3 Graph: x 1

 3  2  1 0123

 1 isin the solution set.

Key Concept

Graphing Inequalities

• Use a circle, , to show that a number is notin the solution set.


• Use a dot, , to show that a number isin the solution set.

Inequality:x 4 or 4 x

(^0123456789) 4 is not in the solution set.
Inequality:x 9 or 9 x
(^12345678910) 9 is in the solution set.
Inequality:x 0 or 0 x
 7  6  5  4  3  2  (^1012) 0 is in the solution set.
Inequality:x 2 or  2 x
 5  4  3  2  (^101234) 2 is not in the solution set.

Acceleration: Graph Compound Inequalities

You can also graph solution sets of compound inequalities.

Graph: 1 x  5 Graph: d 8 or d  6

All numbers between 1 and5 are solutions. All numbers less than 6 orall numbers greater than

or equal to8 are solutions.

0123456789 12345678 10 9

3 is notin the solution set.

0123456

You can write an inequality to describe a given graph in two ways.

These are equivalent inequalities—inequalities that have the same solution set.