Question

tìm số nguyên x biết

a) 25 chia hết cho (2x+1)         b) (18-x) chia hết cho (x-1)

c) (6+x) chia hết cho (x-1)

Answer 1

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Answer 2

a) \(25⋮\left(2x+1\right)\)

\(\Rightarrow2x+1\inƯ\left(25\right)=\left\{-25;-5;-1;1;5;25\right\}\)

\(\Rightarrow2x\in\left\{-26;-6;-2;0;4;24\right\}\)

\(\Rightarrow x\in\left\{-13;-3;-1;0;2;12\right\}\)

Answer 3

c) \(6+x=x-1+7\)

\(\left(6+x\right)⋮\left(x-1\right)\)

\(\Rightarrow\left(x-1+7\right)⋮\left(x-1\right)\)

\(\Rightarrow7⋮\left(x-1\right)\)

\(\Rightarrow x-1\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\)

\(\Rightarrow x\in\left\{-6;0;2;8\right\}\)

Answer 4

b) \(18-x=-\left(x-18\right)=-\left(x-1-17\right)\)

\(\left(18-x\right)⋮\left(x-1\right)\)

\(\Rightarrow\left(x-1-17\right)⋮\left(x-1\right)\)

\(\Rightarrow17⋮\left(x-1\right)\)

\(\Rightarrow x-1\inƯ\left(17\right)=\left\{-17;-1;1;17\right\}\)

\(\Rightarrow x\in\left\{-16;0;2;18\right\}\)