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\(\left(x-1\right)\left(x+5\right)>0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\Rightarrow x>1\\x+5>0\Rightarrow x>-5\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\Rightarrow x< 1\\x+5< 0\Rightarrow x< -5\end{matrix}\right.\end{matrix}\right.\)
\(\left(x-1\right)\left(x+5\right)< 0\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\Rightarrow x>1\\x+5< 0\Rightarrow x< -5\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\Rightarrow x< 1\\x+5>0\Rightarrow x>-5\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow-5< x< 1\)
câu dễ tự làm
\(\Rightarrow x>-5;x< -5\)
\(\text{a) }\left(x-1\right)\left(x-5\right)>0\\ \text{ Để }\left(x-1\right)\left(x-5\right)>0\text{ thì }\Rightarrow x-1\text{ và }x-5\text{ cùng dấu }\\ \text{+) Xét }x-1\text{ và }x-5\text{ là số nguyên dương }\Rightarrow\left\{{}\begin{matrix}x-1>0\Rightarrow x>1\\x-5>0\Rightarrow x>5\end{matrix}\right.\Rightarrow x>5\\ \text{+) Xét }x-1\text{ và }x-5\text{ là số nguyên âm }\Rightarrow\left\{{}\begin{matrix}x-1< 0\Rightarrow x< 1\\x-5< 0\Rightarrow x< 5\end{matrix}\right.\Rightarrow x< 1\\ \text{Vậy }\left(x-1\right)\left(x-5\right)>0\text{ khi }x< 1\text{ hoặc }x>5\)
\(\text{b) }\left(x-1\right)\left(x-5\right)< 0\\ \text{ Để }\left(x-1\right)\left(x-5\right)< 0\text{ thì }\Rightarrow x-1\text{ và }x-5\text{ trái dấu }\\ \text{ Mà }x-1>x-5\\ \Rightarrow\left\{{}\begin{matrix}x-1>0\Rightarrow x>1\\x-5< 0\Rightarrow x< 5\end{matrix}\right.\Rightarrow1< x< 5\\ \text{ Vậy }\left(x-1\right)\left(x-5\right)< 0\text{ khi }1< x< 5\)
\(\text{c) }\dfrac{3}{4}-\dfrac{1}{4}\left|x-\dfrac{1}{7}\right|=\dfrac{1}{4}\\ \Leftrightarrow\dfrac{1}{4}\left|x-\dfrac{1}{7}\right|=\dfrac{1}{2}\\ \Leftrightarrow\left|x-\dfrac{1}{7}\right|=2\\ \Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{7}=-2\\x-\dfrac{1}{7}=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{13}{7}\\x=\dfrac{15}{7}\end{matrix}\right.\\ \text{Vậy }x=-\dfrac{13}{7}\text{ hoặc }x=\dfrac{15}{7}\)
\(\text{d) }\left(x-\dfrac{1}{2}\right)^2=\dfrac{1}{16}\\ \Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=-\dfrac{1}{4}\\x-\dfrac{1}{2}=\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=\dfrac{3}{4}\end{matrix}\right.\\ \text{Vậy }x=\dfrac{1}{4}\text{ hoặc }x=\dfrac{3}{4}\)
\(\text{e) }8\left(x+1\right)-2\left(2x+5\right)=0\\ \Leftrightarrow8x+8-4x+10=0\\ \Leftrightarrow\left(8x-4x\right)+\left(8+10\right)=0\\ \Leftrightarrow4x+18=0\\ \Leftrightarrow4x=-18\\ \Leftrightarrow x=-\dfrac{9}{2}\\ \text{Vậy }x=-\dfrac{9}{2}\)
\(\text{g) }\left(6x-1\right)-\left(x+8\right)=0\\ \Leftrightarrow6x-1-x-8=0\\ \Leftrightarrow\left(6x-x\right)-\left(1+8\right)=0\\ \Leftrightarrow5x-9=0\\ \Leftrightarrow5x=9\\ \Leftrightarrow x=\dfrac{9}{5}\\ \text{Vậy }x=\dfrac{9}{5}\)
\(\text{h) }\left|7x-\dfrac{1}{4}\right|=1\\ \Leftrightarrow\left[{}\begin{matrix}7x-\dfrac{1}{4}=-1\\7x-\dfrac{1}{4}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}7x=-\dfrac{3}{4}\\7x=\dfrac{5}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{28}\\x=\dfrac{5}{28}\end{matrix}\right.\\ \text{Vậy }x=-\dfrac{3}{28}\text{ hoặc }x=\dfrac{5}{28}\)
\(\text{q) }-2x-3=-x+7\\ \Leftrightarrow-2x-3-\left(-x+7\right)=0\\ \Leftrightarrow-2x-3+x-7=0\\ \Leftrightarrow\left(-2x+x\right)-\left(3+7\right)=0\\ \Leftrightarrow-x-10=0\\ \Leftrightarrow-x=10\\ \Leftrightarrow x=-10\\ \text{ Vậy }x=-10\)
Bài 1:
a, \(2y.\left(y-\dfrac{1}{7}\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}2y=0\\y-\dfrac{1}{7}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=0\\y=\dfrac{1}{7}\end{matrix}\right.\)
Vậy \(y\in\left\{0;\dfrac{1}{7}\right\}\)
b, \(\dfrac{-2}{5}+\dfrac{2}{3}y+\dfrac{1}{6}y=\dfrac{-4}{15}\)
\(\Rightarrow\dfrac{5}{6}y=\dfrac{-4}{15}+\dfrac{2}{5}\)
\(\Rightarrow\dfrac{5}{6}y=\dfrac{2}{15}\)
\(\Rightarrow y=\dfrac{4}{25}\)
Vậy \(y=\dfrac{4}{25}\)
Chúc bạn học tốt!!!
Bài 1:
a, \(2y\left(y-\dfrac{1}{7}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2y=0\\y-\dfrac{1}{7}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}y=0\\y=\dfrac{1}{7}\end{matrix}\right.\)
Vậy...
b, \(\dfrac{-2}{5}+\dfrac{2}{3}y+\dfrac{1}{6}y=\dfrac{-4}{15}\)
\(\Rightarrow\dfrac{5}{6}y=\dfrac{2}{15}\)
\(\Rightarrow y=\dfrac{4}{25}\)
Vậy...
Bài 2:
a, \(x\left(x-\dfrac{4}{7}\right)>0\)
\(\Rightarrow\left\{{}\begin{matrix}x>0\\x-\dfrac{4}{7}>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x< 0\\x-\dfrac{4}{7}< 0\end{matrix}\right.\)
\(\Rightarrow x>\dfrac{4}{7}\left(x\ne0\right)\) hoặc \(x< \dfrac{4}{7}\left(x\ne0\right)\)
Vậy...
Các phần còn lại tương tự nhé
a) \(x-\dfrac{2}{3}=\dfrac{3}{8}\Rightarrow x=\dfrac{3}{8}+\dfrac{2}{3}=\dfrac{25}{24}\)
b) \(x-\dfrac{3}{4}=\dfrac{13}{10}:\dfrac{26}{5}\Rightarrow x-\dfrac{3}{4}=\dfrac{1}{4}\Rightarrow x=\dfrac{1}{4}+\dfrac{3}{4}=1\)
c) \(\dfrac{3}{2}-\left(x+\dfrac{1}{2}\right)=\dfrac{4}{5}\Rightarrow x+\dfrac{1}{2}=\dfrac{3}{2}-\dfrac{4}{5}=\dfrac{7}{10}\)
\(\Rightarrow x=\dfrac{7}{10}-\dfrac{1}{2}=\dfrac{1}{5}\)
d) \(\left|x-2\right|-1=0\Rightarrow\left|x-2\right|=1\)
\(\Rightarrow\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
a: Ta có: \(x-\dfrac{2}{3}=\dfrac{3}{8}\)
\(\Leftrightarrow x=\dfrac{3}{8}+\dfrac{2}{3}=\dfrac{9}{24}+\dfrac{16}{24}=\dfrac{25}{24}\)
b: Ta có: \(x-\dfrac{3}{4}=\dfrac{13}{10}:\dfrac{26}{5}\)
\(\Leftrightarrow x-\dfrac{3}{4}=\dfrac{13}{10}\cdot\dfrac{5}{26}=\dfrac{1}{4}\)
hay x=1
3: \(\left|x-\dfrac{3}{4}\right|-\dfrac{1}{2}=0\)
\(\Leftrightarrow\left|x-\dfrac{3}{4}\right|=\dfrac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{1}{2}\\x-\dfrac{3}{4}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{4}\\x=\dfrac{1}{4}\end{matrix}\right.\)
\(\left|\dfrac{7}{8}x+\dfrac{5}{6}\right|-\left|\dfrac{1}{2}x+5\right|=0\\ \Leftrightarrow\left|\dfrac{7}{8}x+\dfrac{5}{6}\right|=\left|\dfrac{1}{2}x+5\right|\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{7}{8}x+\dfrac{5}{6}=\dfrac{1}{2}x+5\\\dfrac{7}{8}x+\dfrac{5}{6}=-\left(\dfrac{1}{2}x+5\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{100}{9}\\-\dfrac{140}{33}\end{matrix}\right.\)
Nhiều quá, từng bài 1 nhé, bài nào làm được, tớ sẽ cố gắng.
bài 2:
a) \(x>2x\Leftrightarrow x-2x>0\Leftrightarrow-x>0\Leftrightarrow x< 0\)
Kl: x<0
b) \(a+x< a\Leftrightarrow x< 0\)
Kl: x<0
c) \(x^3>x^2\Leftrightarrow x^3-x^2>0\Leftrightarrow x^2\left(x-1\right)>0\) (*)
Mà x^2 > 0 \(\Rightarrow\) (*) \(\Leftrightarrow x-1>0\Leftrightarrow x>1\)
Kl: x>1
Câu 4:
a) \(1-2x< 7\Leftrightarrow2x>-6\Leftrightarrow x>3\)
Kl: x>3
b) \(\left(x-1\right)\left(x-2\right)>0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x>2\\x< 1\end{matrix}\right.\)
Kl: x>2 hoặc x<1
c) \(\left(x-2\right)^2\left(x+1\right)\left(x+4\right)< 0\Leftrightarrow\left(x+1\right)\left(x+4\right)< 0\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+1>0\\x+4< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+1< 0\\x+4>0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-1\\x< -4\end{matrix}\right.\\\left\{{}\begin{matrix}x< -1\\x>-4\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}-1< x< -4\left(vô-lý\right)\\-4< x< -1\end{matrix}\right.\) \(\Leftrightarrow-4< x< -1\)
Kl: -4<x<-1
d) ĐK: x khác 9\(\dfrac{x^2\left(x+3\right)}{x-9}< 0\Leftrightarrow x^2\left(x+3\right)\left(x-9\right)< 0\Leftrightarrow\left(x+3\right)\left(x-9\right)< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+3>0\\x-9< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x+3< 0\\x-9>0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-3\\x< 9\end{matrix}\right.\\\left\{{}\begin{matrix}x< -3\\x>9\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}-3< x< 9\left(N\right)\\9< x< -3\left(vô-lý\right)\end{matrix}\right.\) \(\Leftrightarrow-3< x< 9\)
Kl: -3<x<9
e) Đk: x khác 0
\(\dfrac{5}{x}< 1\Leftrightarrow\dfrac{5}{x}< \dfrac{5}{5}\Leftrightarrow x>5\left(N\right)\)
KL: x >5
f) ĐK: x khác 1
\(\dfrac{2x-5}{x-1}< 0\Leftrightarrow\left(2x-5\right)\left(x-1\right)< 0\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-5>0\\x-1< 0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-5< 0\\x-1>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>\dfrac{5}{2}\\x< 1\end{matrix}\right.\\\left\{{}\begin{matrix}x< \dfrac{5}{2}\\x>1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\dfrac{5}{2}< x< 1\left(vô-lý\right)\\1< x< \dfrac{5}{2}\left(N\right)\end{matrix}\right.\)
Kl: 1< x< 5/2
