ssolve 1)x−[x]≥0 2)x−[x]≤0 3)x+[x]≥0 4)x+[x]≤0


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Question Number 86779 by M±th+et£s last updated on 31/Mar/20

$s s o l v e$ $1) x - [x] ⩾ 0$ $2) x - [x] ⩽ 0$ $3) x + [x] ⩾ 0$ $4) x + [x] ⩽ 0$
	Answered by mr W last updated on 31/Mar/20

	$(1)$ $x ⩾ [x]$ $\Rightarrow x ⩾ 0$ $(2)$ $x ⩽ [x]$ $\Rightarrow x ⩽ 0$ $(3)$ $i f x ⩾ 0,$ $[x] = x - δ$ $x + [x] = 2 x - δ ⩾ 0$ $x ⩾ \frac{δ}{2}$ $\Rightarrow x ⩾ 0$ $i f x < 0,$ $[x] = x + 1 - δ$ $x + [x] = 2 x + 1 - δ ⩾ 0$ $x ⩾ - \frac{1}{2} + \frac{δ}{2} ⩾ 0$ $\Rightarrow x ⩾ 0 i s s o l u t i o n$ $(4)$ $i f x ⩾ 0,$ $[x] = x - δ$ $x + [x] = 2 x - δ ⩽ 0$ $x ⩽ \frac{δ}{2} ⩽ 0$ $i f x < 0,$ $[x] = x + 1 - δ$ $x + [x] = 2 x + 1 - 0$ $x ⩽ - \frac{1}{2} + \frac{δ}{2} ⩽ 0$ $\Rightarrow x ⩽ 0 i s s o l u t i o n$
	Commented by M±th+et£s last updated on 31/Mar/20

	$t h a n k y o u s i r$
	Commented by TawaTawa1 last updated on 31/Mar/20

	$Sir, help me with Q 86789$
	Commented by mr W last updated on 31/Mar/20

	$t r y t o s o l v e b y y o u r s e l f a t f i r s t . . .$
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