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9 units from negative 3​

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SOLVING ABSOLUTE VALUE INEQUALITIES

Silvia V. asked • 08/30/16

A number is more than 9 units from 3

i would like to know how to make an inequality

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Arturo O. answered • 08/30/16

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You must account for both the number being more than 9 units smaller than 3 and being more than 9 units larger than 3. To do that, you set the absolute value of the difference between the number and 3 greater than 9.

Let x be the number

|x - 3| > 9

Now solve for x.

Suppose x - 3 is positive. Then

x - 3 > 9 ⇒ x > 12

Suppose x - 3 is negative. Then |x - 3| = -(x - 3) = 3 - x

Then

3 - x > 9 ⇒ x < -6

These are the 2 possibilities.

Step-by-step explanation:

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