Solve and graph the inequality: |x| < 3.

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justaguide eNotes educator | Certified Educator

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The inequality |x| < 3 can be written as

-3 < x < 3

To draw the graph of the inequality consider all points of x that lie between -3 and +3 but do not include -3 and +3.

This gives all the value that x can take as those that lie in the set (-3 , 3).

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giorgiana1976 | Student

To solve the inequality, we'll have to apply the definition of the absolute value:

|x|<c <=> -c<x<c

For c = 3 => -3 < x < 3

We'll solve the simultaneous inequalities:

-3 < x and x < 3

-3 < x <=> x belongs to the range (-3 ; +infinite)

x < 3 <=> x belongs to the range (-infinite ; 3)

We'll intercept the intervals and the common solution for x is found in the opened interval (-3 ; 3).

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