Question

explica modulul
|x-2|  ,  |1-x|  ,  |3x-6| ,  |10-5x|

Answer 1

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|x-2| = x - 2 daca x-2 > 0 =>  |x-2| = x - 2 daca x > 2
|x-2| = 0 daca x - 2 = 0    =>  |x-2| = 0 daca x = 2
|x-2| = - (x - 2) = 2 - x daca x - 2 < 0  => |x-2| = - (x - 2) = 2 - x daca x < 2
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|1-x| = 1 - x daca 1 - x > 0  => |1-x| = 1 - x daca x < 1
|1-x| = 0 daca  1 - x = 0  => |1-x| = 0 daca  x = 1
|1-x| = -(1 - x) = x - 1  daca  1 - x < 0  => |1-x| = x - 1 daca x > 1
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|3x-6| = 3x + 6 daca 3x + 6 > 0  => |3x-6| = 3x + 6 daca x > -2
|3x-6| = 0 daca  3x + 6 = 0  => |3x-6| = 0 daca  x = -2
|3x-6| = -(3x + 6) = -3x - 6 daca 3x + 6 < 0  => |3x-6| = -3x - 6 daca x < -2
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|10-5x| = 10 - 5x  daca  10 - 5x > 0  => |10-5x| = 10 - 5x  daca  x < 2
|10-5x| = 0  daca  10 - 5x = 0  => |10-5x| = 0  daca  x = 2
|10-5x| = -(10 - 5x) = 5x - 10 daca 10 - 5x < 0  => |10-5x| = 5x - 10  daca  x > 2
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