6th Grade Math Textbook, Fundamentals

Lesson 3-1 for exercise sets. &KDSWHU 

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For an inequality with the symbol or , test both parts of the inequality symbol:

• If at least one of the closed sentences is true, the inequality is true for that value
  of the variable.


• If both closed sentences are false, the inequality is false for that value
  of the variable.

x2, when x 5

Test: 5 2 Substitute 5 for x.

5  2 The closed sentence is true.

The inequality is true for x5.

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1 a2, when a 4

Test: 4 2 Substitute 4 for a.

4  2 The closed sentence is false.

The inequality is false for a4.

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2

m 9, when m 1

Test: 1 9 Substitute 1 for m. Tr u e Test: 1 9 Substitute 1 for m. False

Since one closed sentence is true, the inequality is true for m1.

? ?

3

g 11, when g  7

Test: 7 11 Substitute 7 for g. False Test: 7 11 Substitute 7 for g. False

Since both closed sentences are false, the inequality is false for g7.

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4

Tell whether the inequality is true or false for the given value.

A is an inequality that consists of two or more inequalities

that are connected. The following inequality expresses two related statementsjoined

by the word and.

Word Sentence Two Inequalities Compound Inequality

Kim is older than her 6-year-old Let kKim’s age. 6 k  15

sister, and Kim is younger than her k 6 and k 15

15-year-old brother.

Read as kis greater than 6

and is less than15.

compound inequality

Write each as an inequality. Write each as a word sentence.

1.Tony is at least fourteen years old.

2.Negative eight increased by a number

is greater than or equal to twenty.

3.A number, x, is greater than or equal

to 6 and is less than 12.

7.Discuss and Write Explain why x

4 is false when x0.

4.x 8  32

5.|7| 

9 n

6. (4) z 9