Insert <, >, or = in the appropriate space to make a true statement. See Examples 6...

Insert <, >, or = in the appropriate space to make a true statement. See Examples 6 through 8.

EXAMPLE 6 Insert <, >, or = in the appropriate space to make each statement true.

a.

−1

0

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b.

7

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c.

−5

−6

Solution

a. −1 < 0 since −1 is to the left of 0 on a number line.

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b. since simplifies to 7.

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c. −5 > −6 since −5 is to the right of −6 on the number line.

EXAMPLE 7 Find the absolute value of each number.

a. |4|

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b. |−5|

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c. |0|

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d.

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e. |5.6|

Solution

a. |4| = 4 since 4 is 4 units from 0 on a number line.

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b. |−5| = 5 since −5 is 5 units from 0 on a number line.

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c. |0| = 0 since 0 is 0 units from 0 on a number line.

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d. since is unit from 0 on a number line.

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e. |5.6| = 5.6 since 5.6 is 5.6 units from 0 on a number line.

EXAMPLE 8 Insert <, >, or = in the appropriate space to make each statement true.

a.

|0|

2

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b.

|−5|

5

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c.

|−3|

|−2|

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d.

|5|

|6|

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e.

|−7|

|6|

Solution

a. |0| < 2 since |0| = 0 and 0 < 2.

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b. |−5| = 5 since 5 = 5.

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c. |−3| > |−2| since 3 > 2.

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d. |5| < |6| since 5<6.

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e. |−7| > |6| since 7 > 6.