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Question

The minimum value of the expression y=|x+3|+|x+1|+|x5| is

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Solution

y=|x+3|+|x+1|+|x5|
Here the turning points are 3,1,5

|x+3|+|x+1|+|x5|=⎪ ⎪ ⎪⎪ ⎪ ⎪(x+3)(x+1)(x5),x<3(x+3)(x+1)(x5),3x<1(x+3)+(x+1)(x5),1x<5(x+3)+(x+1)+(x5),x5

|x+3|+|x+1|+|x5|=⎪ ⎪⎪ ⎪13x,x<37x,3x<19+x,1x<53x1,x5


Hence, the minimum value of the given expression is 8.

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