SOLUTION: Help me answer this question please: ⌊1.25 + ⌊𝑥⌋⌋ = 12 I am completely unsure as I have no clue what that style of brakcets mean

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Question 1106550: Help me answer this question please:
⌊1.25 + ⌊𝑥⌋⌋ = 12
I am completely unsure as I have no clue what that style of brakcets mean

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Those brackets indicate the "floor" function.
floor(x) = k where k is the greatest integer less than or equal to x; x is a real number, k is an integer.

The question is asking to find x such that the floor( floor(x) + 1.25 ) = 12

The inner-most floor (floor(x)) is an integer, so we can re-write this problem using integer n:
floor(n + 1.25) = 12

if n = 10 we get floor(10 + 1.25) = floor(11.25) = 11 too low
if n = 11 we get floor(11 + 1.25) = floor(12.25) = 12 ok
Since the inner-most floor (floor(x)) is taken first in order to get the 11 in 11+1.25, x can be any value in the range

——
Check:
x=11: floor(x) = floor(11) = 11 and floor(11+1.25) = floor(12.25) = 12 (ok)
x=12-s where 0 < s <= 1: floor(x) = floor(12-s) = floor(some number greater than or equal to 11, and less than 12) = 11 and floor(11+1.25) = floor(12.25) = 12 (ok)
You can also do negative checks by letting x=11-s and x=12 to see that those do not result in a final value of 12, to convince yourself the highlighted range captures all possible values of x.

One thing about the floor() function, you must be very careful about your less than or equal signs.
A related function is the ceiling() function.



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