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Question

The number of integral values of x satisfying the linear inequality |x|+|x+1| < 5 is .

A
3
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B
4
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C
5
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D
6
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Solution

The correct option is B 4
Given that |x|+|x+1| < 5.
Now, (x|=(x, if x0x if x<0(x+1|=(x+1, if x1x1 if x<1(x|+(x+1|=x+x+1=2x+1, if x0x+x+1=1, if 1< x<0xx1=2x1, if x1Now, (x|+(x+1|<5Case I: If x0(x|+(x+1|=2x+12x+1<5x<2x=0, 1Case II: If 1< x<0(x|+(x+1|=1 which is less than 5.No integral value of x in this interval.Case III: If x1(x|+(x+1|=2x12x1<52x<6x>3x=2, 1
Therefore, the integral values of x satisfying the given linear inequation is -2, -1, 0, 1.
Number of values = 4

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