Question

(x+1) (x-2) (lxl-3)/x(x-5)<= 0

Answer 1

Answer:

THIS IS YOUR CORRECT ANSWER. HAVE A GOOD DAY.

Step-by-step explanation:

A. x<−1x<−1 (blue range) --> |x+1|=2|x−1||x+1|=2|x−1| becomes: −x−1=2(−x+1)−x−1=2(−x+1) --> x=3x=3, not OK, as this value is not in the range we are checking (x<−1x<−1);

B. −1≤x≤1−1≤x≤1 (green range) --> |x+1|=2|x−1||x+1|=2|x−1| becomes: x+1=2(−x+1)x+1=2(−x+1) --> x=13x=13. OK, as this value is in the range we are checking (−1≤x≤1−1≤x≤1);

C. x>1x>1 (red range) --> |x+1|=2|x−1||x+1|=2|x−1| becomes: x+1=2(x−1)x+1=2(x−1) --> x=3x=3. OK, as this value is in the range we are checking (x>1x>1).

So we got TWO values of xx (two solutions): 1313 and 33, first is in the range (-1,1) but second is out of the range. Not sufficient.

(2) |x−3|≠0|x−3|≠0

Just says that x≠3x≠3. But we don't know whether xx is in the range (-1,1) or not.

(1)+(2) x=13x=13 or x=3x=3 AND x≠3x≠3 --> means xx can have only value 1313, which is in the range (-1,1). Sufficient.

Answer: C.

Hope it helps.

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