# Solve for x in l x-3 l < 3.

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l x-3 l < 3

We have two cases:

(x-3) < 3      and    -(x-3) < 3

x < 6             and (x-3) > -3

x< 6             and    x > 0

Then the solution is:

0 < x < 6

OR:  x belong to the interval (0, 6)

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The inequality l x-3 l < 3 could be written as:

-3 < x-3 < 3

We'll solve the left side of the inequality:

-3 < x-3

We'll add 3 both sides, in order to isolate x:

-3 + 3 < x

0 < x

Now, we'll solve the right side of the inequality:

x-3 < 3

x < 3 + 3

x < 6

The values of x which satisfies the inequality l x-3 l < 3 are located in the interval (0 , 6).

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|x-3| <3. To find the solution for x.

Solution:

|x-3|  means  x-3 when x>3: So when x > 3, the ineequation is   x -3 < 3  . Or x < 3+6 = .

So x < 6.......................(1)

|x-3| means 3-x when x<3: Therefore when x<3, the inequation becomes 3-x < 3 . Or  3- 3- x  < 0. Or

0-x < 0. Or

x > 0............................(2)

Combining (1) and (2) we get:

0 <x < 6. So x is in the open interval (0 , 6).

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