`2x-2/3=1/2`

`2x=1/2+2/3`

`2x=7/6`

`x=7/6:2=7/12`

\(2x-\dfrac{2}{3}=\dfrac{1}{2}\Leftrightarrow2x=\dfrac{2}{3}+\dfrac{1}{2}=\dfrac{7}{6}\Leftrightarrow x=\dfrac{7}{6}:2=\dfrac{7}{12}\)

2x - 2/3 = 1/2

2x = 1/2 + 2/3 = 7/6

x = 7/6 : 2 = 7/12

vậy x = 7/12

28A

30 B

40B

\(a,m=3\Leftrightarrow y=2x+2\\ A\left(a;-4\right)\in\left(d\right)\Leftrightarrow2a+2=-4\Leftrightarrow a=-3\)

\(b,\) PT giao Ox của (d) là \(2x+m-1=0\Leftrightarrow x=\dfrac{1-m}{2}\Leftrightarrow M\left(\dfrac{1-m}{2};0\right)\Leftrightarrow OM=\dfrac{\left|1-m\right|}{2}\)

PT giao Oy của (d) là \(x=0\Leftrightarrow y=m-1\Leftrightarrow N\left(0;m-1\right)\Leftrightarrow ON=\left|m-1\right|\)

Để \(S_{OMN}=1\Leftrightarrow\dfrac{1}{2}OM\cdot ON=1\Leftrightarrow OM\cdot ON=2\)

\(\Leftrightarrow\dfrac{\left|\left(1-m\right)\left(m-1\right)\right|}{2}=2\\ \Leftrightarrow\left|-\left(m-1\right)^2\right|=2\\ \Leftrightarrow\left(m-1\right)^2=2\\ \Leftrightarrow\left[{}\begin{matrix}m=1+\sqrt{2}\\m=1-\sqrt{2}\end{matrix}\right.\)

8.

Gọi \(A\left(x_0;y_0\right)\) là điểm cố định mà đt luôn đi qua với mọi m

\(\Leftrightarrow mx_0+2y_0-3my_0+m-1=0\\ \Leftrightarrow m\left(x_0-3y_0+1\right)+\left(2y_0-1\right)=0\\ \Leftrightarrow\left\{{}\begin{matrix}x_0-3y_0+1=0\\2y_0-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x_0=\dfrac{1}{2}\\y_0=\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow A\left(\dfrac{1}{2};\dfrac{1}{2}\right)\)

Vậy đt luôn đi qua \(A\left(\dfrac{1}{2};\dfrac{1}{2}\right)\) với mọi m

9.

PT giao Ox là \(y=0\Leftrightarrow mx+m-1=0\Leftrightarrow x=\dfrac{1-m}{m}\Leftrightarrow A\left(\dfrac{1-m}{m};0\right)\Leftrightarrow OA=\left|\dfrac{1-m}{m}\right|\)

PT giao Oy là \(x=0\Leftrightarrow\left(2-3m\right)y+m-1=0\Leftrightarrow y=\dfrac{1-m}{2-3m}\Leftrightarrow B\left(0;\dfrac{1-m}{2-3m}\right)\Leftrightarrow OB=\left|\dfrac{1-m}{2-3m}\right|\)

Để \(\Delta OAB\) cân thì \(OA=OB\Leftrightarrow\left|\dfrac{1-m}{m}\right|=\left|\dfrac{1-m}{2-3m}\right|\)

\(\Leftrightarrow\left|m\right|=\left|2-3m\right|\Leftrightarrow\left[{}\begin{matrix}m=2-3m\\m=3m-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m=\dfrac{1}{2}\\m=1\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}m=\dfrac{1}{2}\\m=1\end{matrix}\right.\) thỏa mãn đề

tui chịu luôn đó

Câu 1 này bình phương hơi dài dòng nên khử trị tuyệt đối sẽ tốt hơn:

\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x^2-2x-3\ge0\\x^2-2x-3\ge3x-3\end{matrix}\right.\\\left\{{}\begin{matrix}x^2-2x-3< 0\\-\left(x^2-2x-3\right)\ge3x-3\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge3\\x\le-1\end{matrix}\right.\\x^2-5x\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}-1< x< 3\\x^2+x-6\le0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge3\\x\le-1\end{matrix}\right.\\\left[{}\begin{matrix}x\ge5\\x\le0\end{matrix}\right.\end{matrix}\right.\\\left\{{}\begin{matrix}-1< x< 3\\-3\le x\le2\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge5\\x\le-1\end{matrix}\right.\\-1< x\le2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\ge5\\x\le2\end{matrix}\right.\)

Vậy C đúng