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# What is the minimum value of |x - 3| + |x + 3| ?

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Re: What is the minimum value of |x - 3| + |x + 3| ? [#permalink]
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Bunuel wrote:
What is the minimum value of $$|x-3|+|x+3|$$?

(A) 0
(B) 3
(C) 6
(D) 8
(E) 12

$$|x-3|+|x+3|$$
Whenever x>3, the values of MOD will keep increasing as x increases in both the MODS.
Whenever x<-3, the values of MOD will keep increasing again as x decreases in both the MODS but ultimately results in positive x.
But whenever $$-3\leq x\leq 3$$, one x gets subtracted from 3/-3 and other gets added to -3/3, resulting in no effect of x on the SUM.

So, value is |-3|+|3| =3+3 = 6.

You can also think of it as a number line.
..........-3.........3..........
If x is between -3 and 3 => .......-3.....x......3......, the distance is 3 to -3 or 6.
If x<-3, ....x.........-3..........3......, the distance is (3 to x) + (-3 to x), that is (3 to -3) + 2 times distance from -3 to x..

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Re: What is the minimum value of |x - 3| + |x + 3| ? [#permalink]
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Bunuel wrote:
What is the minimum value of $$|x-3|+|x+3|$$?

(A) 0
(B) 3
(C) 6
(D) 8
(E) 12

The modulus function graph has inflexion at x=3 and x=-3

and increases to give a positive value greater than minimum

The minmum occurs at x=3 or -3 yielding 6

THerefore IMO C
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Re: What is the minimum value of |x - 3| + |x + 3| ? [#permalink]
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Re: What is the minimum value of |x - 3| + |x + 3| ? [#permalink]
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