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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 byM±th+et£s last updated on 11/Apr/20

god bless you sir

$${god}\:{bless}\:{you}\:{sir} \\ $$

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