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If-4x-3-Mod-6-find-the-first-four-values-of-x-




Question Number 140428 by byaw last updated on 07/May/21
If 4x=3(Mod 6), find the  first four values of x.
$$\mathrm{If}\:\mathrm{4}{x}=\mathrm{3}\left(\mathrm{Mod}\:\mathrm{6}\right),\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{four}\:\mathrm{values}\:\mathrm{of}\:{x}. \\ $$
Commented by mr W last updated on 07/May/21
4x is even.  but when it is divided by 6 and the  remainder is 3, it means 4x must be  odd. a number can not be even and odd  at same time. therefore there is no  solution, i.e. the question is wrong.
$$\mathrm{4}{x}\:{is}\:{even}. \\ $$$${but}\:{when}\:{it}\:{is}\:{divided}\:{by}\:\mathrm{6}\:{and}\:{the} \\ $$$${remainder}\:{is}\:\mathrm{3},\:{it}\:{means}\:\mathrm{4}{x}\:{must}\:{be} \\ $$$${odd}.\:{a}\:{number}\:{can}\:{not}\:{be}\:{even}\:{and}\:{odd} \\ $$$${at}\:{same}\:{time}.\:{therefore}\:{there}\:{is}\:{no} \\ $$$${solution},\:{i}.{e}.\:{the}\:{question}\:{is}\:{wrong}. \\ $$
Answered by JDamian last updated on 07/May/21
4x=6q+3    As the left side (4x) is even, the rigth one  should be too... but   6q+3    is odd...
$$\mathrm{4}{x}=\mathrm{6}{q}+\mathrm{3} \\ $$$$ \\ $$$${As}\:{the}\:{left}\:{side}\:\left(\mathrm{4}{x}\right)\:{is}\:{even},\:{the}\:{rigth}\:{one} \\ $$$${should}\:{be}\:{too}…\:{but}\:\:\:\mathrm{6}{q}+\mathrm{3}\:\:\:\:{is}\:\boldsymbol{{odd}}… \\ $$

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