if y = [ 2x+5 ] = 3[x−4] then [ 3x+y ] = ?


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Question Number 95309 by i jagooll last updated on 24/May/20

$if y = [2 x + 5] = 3 [x - 4]$ $then [3 x + y] = ?$
	Answered by mr W last updated on 24/May/20

	$l e t u = x - 4 = n + f w i t h 0 ⩽ f < 1$ $2 x + 5 = 2 (4 + n + f) + 5 = 2 (4 + n) + 5 + 2 f$ $c a s e 0 ⩽ f < \frac{1}{2} :$ $y = [2 x + 5] = 2 (4 + n) + 5 + [2 f] = 13 + 2 n = 3 n$ $\Rightarrow n = 13$ $\Rightarrow x = 4 + n + f = 17 + f$ $i . e . 17 ⩽ x < 17.5$ $[3 x + y] = 51 + [3 f] + 39 = 90 + [3 f [= 90 o r 91$ $c a s e \frac{1}{2} ⩽ f < 1 :$ $y = [2 x + 5] = 2 (4 + n) + 5 + [2 f] = 14 + 2 n = 3 n$ $\Rightarrow n = 14$ $\Rightarrow x = 4 + n + f = 18 + f$ $i . e . 18.5 ⩽ x < 19$ $[3 x + y] = 54 + [3 f] + 42 = 96 + [3 f [= 97 o r 98$ $\Rightarrow [3 x + y] = 90, 91, 97, 98 .$
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