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If the equation |2 - x| - |x + 1|= k has...

If the equation `|2 - x| - |x + 1|= k` has exactly one solution, then number of integral values of `k` is (A) 7 (B) 5 (C) 4 (D) 3

A

7

B

5

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
Let f(x) = |x - 2| - |x +1|= `{{:(3 ,"," x lt -1) ,(-2x + 1, "," -1 lexle2), (-3 ,"," x gt 2):}

So, k `in (-3,3)`
`therefore k_(integers) = -2 , -1 , 0 , 1, 2`
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