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Question Number 88555 by M±th+et£s last updated on 11/Apr/20
slove   ⌈(x/a)⌉<a     when a>1  ⌈...⌉ is ceil function
$${slove}\: \\ $$$$\lceil\frac{{x}}{{a}}\rceil<{a}\:\:\: \\ $$$${when}\:{a}>\mathrm{1} \\ $$$$\lceil…\rceil\:{is}\:{ceil}\:{function} \\ $$
Answered by mr W last updated on 11/Apr/20
⌈(x/a)⌉=n<a  ⌈(x/a)⌉=n<⌈a⌉−1  (x/a)≤n  x≤na<(⌈a⌉−1)a  ⇒solution is x<(⌈a⌉−1)a
$$\lceil\frac{{x}}{{a}}\rceil={n}<{a} \\ $$$$\lceil\frac{{x}}{{a}}\rceil={n}<\lceil{a}\rceil−\mathrm{1} \\ $$$$\frac{{x}}{{a}}\leqslant{n} \\ $$$${x}\leqslant{na}<\left(\lceil{a}\rceil−\mathrm{1}\right){a} \\ $$$$\Rightarrow{solution}\:{is}\:{x}<\left(\lceil{a}\rceil−\mathrm{1}\right){a} \\ $$
Commented by M±th+et£s last updated on 11/Apr/20
god bless you sir
$${god}\:{bless}\:{you}\:{sir} \\ $$

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