Question

[Nguyen thi thanh Huyen]

Tìm x, sao cho:

a) 1 - 2*x < 7

b) (x - 1)*(x - 2) > 0

c) ( x - 2)^2*(x + 1)*(x - 4) < 0

d) x^2*(x - 3) / x - 9 < 0

e) 5/x < 1

Answer 1

[Vũ Minh Tuấn]

e) \(\frac{5}{x}< 1.\)

Để \(\frac{5}{x}< 1\Leftrightarrow\frac{5}{x}\le0.\)

\(\Rightarrow\left\{{}\begin{matrix}\frac{5}{x}=0\\\frac{5}{x}< 0\end{matrix}\right.\)

Mà \(5>0.\)

\(\Rightarrow\frac{5}{x}\ne0.\)

\(\Rightarrow\frac{5}{x}< 0.\)

\(\Rightarrow\) Tử mẫu phải trái dấu

\(\Rightarrow x< 0.\)

Vậy \(x< 0\) thì \(\frac{5}{x}< 1.\)

Chúc bạn học tốt!

Answer 2

[@Nk>↑@]

a)\(1-2x< 7\Leftrightarrow-2x< 6\Leftrightarrow x>-3\)

b)\(\left(x-1\right)\left(x-2\right)>0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-1>0\\x-2>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>1\\x>2\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x>2\\x< 1\end{matrix}\right.\)

c)\(\left(x-2\right)^2.\left(x+1\right).\left(x-4\right)< 0\)

\(\Leftrightarrow\left(x+1\right)\left(x-4\right)< 0\) (vì \(\left(x-2\right)^2\ge0\))

\(\Leftrightarrow\left\{{}\begin{matrix}x+1< 0\\x-4>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x+1>0\\x-4< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< -1\\x>4\end{matrix}\right.\)(loại) hoặc \(\left\{{}\begin{matrix}x>-1\\x< 4\end{matrix}\right.\)(chọn)

\(\Leftrightarrow-1< x< 4\)

d)\(\frac{x^2.\left(x-3\right)}{x-9}< 0\)(ĐK:\(x\ne9\))

\(\Leftrightarrow\frac{x-3}{x-9}< 0\)(vì \(x^2\ge0\))

\(\Leftrightarrow\left\{{}\begin{matrix}x-3< 0\\x-9>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x-3>0\\x-9< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< 3\\x>9\end{matrix}\right.\)(loại) hoặc \(\left\{{}\begin{matrix}x>3\\x< 9\end{matrix}\right.\)

\(\Leftrightarrow3< x< 9\)

e)\(\frac{5}{x}< 1\)(ĐK:\(x\ne0\))

\(\Leftrightarrow\frac{5}{x}-1< 0\)

\(\Leftrightarrow\frac{5-x}{x}< 0\)

\(\Leftrightarrow\left\{{}\begin{matrix}5-x< 0\\x>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}5-x>0\\x< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>5\\x>0\end{matrix}\right.\) hoặc \(\left\{{}\begin{matrix}x< 5\\x< 0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x>5\\x< 0\end{matrix}\right.\)

Giải là phải giải cho hết chứ :)