Question

Which set of numbers best describes the possible values of x in the equation below?[x-1]=[x] all integer values of x all real number values of x only negative values of x only fractional values of x

Answer 1

Answer Choices:

A) all integer values of x

B) all real number values of x

C) only negative values of x

D) only fractional values of x

Answer:

D

This is the correct answer on E2020.

Answer 2

[x] represents floor function also called as Greatest integer function.

Floor function is the function that takes as input a real number and gives as output the greatest integer less than or equal to.

like [1.5]=1

[0.7]=0

[-0.3]=-1

Now we have to find set of x-values which satisfies equation [x-1]=[x]

Due to -1 in [x-1], it always produces output value one less than value of [x]

for example when x=0.5 then [x]=[0.5]=0, [x-1]=[0.5-1]=[-0.5]=-1

when x=1.5 then [x]=[1.5]=1, [x-1]=[1.5-1]=[0.5]=0

when x=3 then [x]=[3]=3, [x-1]=[3-1]=[2]=2

From above results we can see that there is no value of x which satisfies the given equation [x-1]=[x]

Hence there is NO solution.