Bài 1: Tìm tập hợp các số nguyên x để:
a, 3x-5 chia hết cho 2x+1
b, 2x-3 chia hết cho x+1
c, 3x+2 chia hết cho 2x-1
d, 2x-1 chia hết cho x+3
Bài 2:tìm các số nguyên x, y sao cho:
|x-1| ≤ 2
Giải nhanh giúp mình nha
15 người đầu tiên sẽ đc chọn đúng
Bài 1:
a, \(3x-5⋮2x+1\)
\(\Rightarrow2\left(3x-5\right)-3\left(2x+1\right)⋮2x+1\)
\(\Rightarrow6x-10-6x-3⋮2x+1\)
\(\Rightarrow7⋮2x+1\)
\(\Rightarrow2x+1\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow2x\in\left\{0;-2;6;-8\right\}\)
\(\Rightarrow x\in\left\{0;-1;3;-4\right\}\)
b, \(2x-3⋮x+1\)
\(\Rightarrow2x-3-2\left(x+1\right)⋮x+1\)
\(\Rightarrow2x-3-2x-2⋮x+1\)
\(\Rightarrow1⋮x+1\)
\(\Rightarrow x+1\inƯ\left(1\right)=\left\{\pm1\right\}\)
\(\Rightarrow x\in\left\{0;-2\right\}\)
c, \(3x+2⋮2x-1\)
\(\Rightarrow2\left(3x+2\right)-3\left(2x-1\right)⋮2x-1\)
\(\Rightarrow6x+4-6x+3⋮2x-1\)
\(\Rightarrow7⋮2x-1\)
\(\Rightarrow2x-1\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow2x\in\left\{2;0;8;-6\right\}\)
\(\Rightarrow x\in\left\{1;0;4;-3\right\}\)
d, \(2x-1⋮x+3\)
\(\Rightarrow2x-1-2\left(x+3\right)⋮x+3\)
\(\Rightarrow2x-1-2x-6⋮x+3\)
\(\Rightarrow-5⋮x+3\)
\(\Rightarrow x+3\inƯ\left(-5\right)=\left\{\pm1;\pm5\right\}\)
\(\Rightarrow x\in\left\{-2;-4;2;-8\right\}\)
Bài 2:
\(\left|x-1\right|\le2\)
\(\Rightarrow-2\le x-1\le2\)
\(\Rightarrow-2+1\le x-1+1\le2+1\)
\(\Rightarrow-1\le x\le3\)
=> x = {-1;0;1;2;3}
* Trả lời:
Bài 2:
\(\left|x-1\right|\le2\)
\(\Rightarrow x-1\le2\) hoặc \(x-1\le-2\)
\(\Rightarrow x\le3\) | \(x\le-1\)
\(\Rightarrow x\inƯ\left\{3\right\}\) | \(x\inƯ\left\{-1\right\}\)
\(\Rightarrow x\in\left\{3;-3;1;-1\right\}\) | \(x\in\left\{-1;1\right\}\)
Vậy \(x\in\left\{3;-3;1;-1\right\}\)