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08 Feb 2021, 06:45
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Which of the following CANNOT be the value of x - |x| ?
A. 0
B. 2x
C. Value greater than x
D. Value smaller than x
E. x
A. 0
B. 2x
C. Value greater than x
D. Value smaller than x
E. x
08 Feb 2021, 06:56
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A. At x=0, x - |x| = 0. Possible
B. At x=-2, x - |x| = -4 = 2x. Possible
C. Value greater than x
D. Same example shown above in B. Possible
E. Same example as shown above in A. Possible
Ans is C IMO
B. At x=-2, x - |x| = -4 = 2x. Possible
C. Value greater than x
D. Same example shown above in B. Possible
E. Same example as shown above in A. Possible
Ans is C IMO
09 Feb 2021, 01:24
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x - |x|
Critical value approach
Two scenarios for the modulus: x<0; 0≤x
When x<0 the modulus will become -(x)
x--(x)=x+x=2x
When 0≤x the modulus will become (x)
x-(x)=0
A. 0 (X) Answer to the second scenario
B. 2x (X) Answer to the first scenario
C. Value greater than x (0) if x is positive then x<2x. BUT we only got 2x when x is negative. When x is positive we get 0. 0<x.
D. Value smaller than x (X) If x is positive then 0<x
E. x (X) when x=0 then 0=0 and 2x=0
Critical value approach
Two scenarios for the modulus: x<0; 0≤x
When x<0 the modulus will become -(x)
x--(x)=x+x=2x
When 0≤x the modulus will become (x)
x-(x)=0
A. 0 (X) Answer to the second scenario
B. 2x (X) Answer to the first scenario
C. Value greater than x (0) if x is positive then x<2x. BUT we only got 2x when x is negative. When x is positive we get 0. 0<x.
D. Value smaller than x (X) If x is positive then 0<x
E. x (X) when x=0 then 0=0 and 2x=0
