If the solution set of |2x−1|+|3x−4|=|5x−5| is x∈(−∞,p]∪[43,∞), then the value of p is
A
1
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B
12
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C
2
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D
0
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Solution
The correct option is B12 |2x−1|+|3x−4|=|5x−5|
Here 5x−5=(2x−1)+(3x−4)
So, (2x−1)(3x−4)≥0 (∵|x+y|=|x|+|y|,then xy≥0) ⇒(x−12)(x−43)≥0∴x∈(−∞,12]∪[43,∞)
Hence the value of p is 12