1. Smoke / factories / a cause / air pollution
=> Smoke from factories is a cause of air pollution.
2. There / be / fine days / winter / when / sun / shine
=> There are fine days in winter when the sun shines.
3. Lan / have / small field / and / grow / vegetables / flowers
=> Lan has a small field and she grows vegetables and flowers.
4. I / like / fried rice / glass / orange juice, please
=> I would like fried rice and a glass of orange juice, please
5. villagers / like / go / forest when / spring come
=> The villagers like going to the forest when spring comes.
@Trần Ngọc Phương Linh

5. |(x - 1)(2 - y)| = (x - 1)(y - 2)
Xét 2 TH
TH1: (x - 1)(2 - y) = (x - 1)(y - 2)
<=> (x - 1)2 - (x-1)y = (x - 1)y - (x - 1)2
<=> 2x - 2 - xy + 1 = xy - 1 - 2x + 2
<=> 2x - xy - xy + 2x = -1 - 2 + 2 - 1
<=> x(2 - y - y + 2) = -2
<=> x(4 - 2y) = -2
Do x; y thuộc Z => 4 - 2y thuộc Z
Mà x(4 - 2y) = -2
=> x; 4 - 2y thuộc Ư(2) = {-1; 1; -2; 2}
Ta thấy 4 - 2y chẵn => 4 - 2y = -2; 2
Nếu \(\left\{{}\begin{matrix}x=1\\4-2y=-2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\2y=6\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=3\end{matrix}\right.\) (thỏa mãn)

Nếu \(\left\{{}\begin{matrix}x=-1\\4-2y=2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=-1\\2y=2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=1\end{matrix}\right.\) (thỏa mãn)

Vậy các cặp (x; y) thỏa mãn là (1; 3); (-1; 1)
@Phan Đức Gia Linh

4. 2x - |1 - 2x| = 1
<=> |1 - 2x| = 2x - 1
Do |1 - 2x| \(\ge\) 0 => 2x - 1 \(\ge\) 0 => x \(\ge\dfrac{1}{2}\)
Vậy x \(\ge\dfrac{1}{2}\) thì 2x - |1 - 2x|
@Phan Đức Gia Linh

3. |x - 1| - x = - 1
<=> |x - 1| = -1 + x
Do |x - 1| \(\ge\) 0 => -1 + x \(\ge\) 0 => x \(\ge\) 1
Vậy x \(\ge\) 1 thì |x - 1| - x = -1
@Phan Đức Gia Linh

số bé là 50 , sô lớn la 450

1. |x| - x = 0
<=> |x| = x
<=> \(\left[{}\begin{matrix}x=x\\x=-x\end{matrix}\right.\) (thỏa mãn)
@Phan Đức Gia Linh

\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\Leftrightarrow\dfrac{2}{42}+\dfrac{2}{56}+\dfrac{1}{72}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\Leftrightarrow\dfrac{2}{6.7}+\dfrac{2}{7.8}+\dfrac{2}{8.9}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)

\(\Leftrightarrow2\left(\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{2}{9}\)

\(\Leftrightarrow2\left(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2}{9}\)

\(\Leftrightarrow\dfrac{1}{6}-\dfrac{1}{x+1}=\dfrac{1}{9}\)

\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{18}\)

<=> x + 1 = 18
<=> x = 17
@Phan Đức Gia Linh

5. 2 + 4 + 6 + ... + 2x = 210
<=> 2(1 + 2 + 3 + ... + x) = 210
<=> 1 + 2 + 3 + ... + x = 105
<=> (1 + x)[(x - 1) : 1 + 1] : 2 = 105
<=> (1 + x)x = 210
Mà x; x + 1 là 2 số tự nhiên liên tiếp => x = 14
@Phan Đức Gia Linh

4. (6 - x)²⁰¹⁴ = (6 - x)²⁰¹⁵
<=> \(\left[{}\begin{matrix}6-x=0\\6-x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=5\end{matrix}\right.\) (thỏa mãn)
Vậy x = 6; 5
@Phan Đức Gia Linh