1)$\frac{x-5}{y-1}$ <0 2)2x-3-$\frac{1}{x-5}$

15/11/2021

By Athena

1)$\frac{x-5}{y-1}$ <0 2)2x-3-$\frac{1}{x-5}$ { "@context": "https://schema.org", "@type": "QAPage", "mainEntity": { "@type": "Question", "name": " 1)$ frac{x-5}{y-1}$ <0 2)2x-3-$ frac{1}{x-5}$

Đáp án:

 4) \(x <  – \dfrac{1}{5}\)

Giải thích các bước giải:

\(\begin{array}{l}
1)\left[ \begin{array}{l}
\left\{ \begin{array}{l}
x – 5 > 0\\
y – 1 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x – 5 < 0\\
y – 1 > 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x > 5\\
y < 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x < 5\\
y > 1
\end{array} \right.
\end{array} \right.\\
2)DK:x \ne 5\\
2x – 3 – \dfrac{1}{{x – 5}} < x – 4 – \dfrac{1}{{x – 5}}\\
 \to 2x – 3 < x – 4\\
 \to x <  – 1\\
3)4x + 8 < 1 – x\\
 \to 5x <  – 7\\
 \to x <  – \dfrac{7}{5}\\
4)x + 3 < 2 – 4x\\
 \to 5x <  – 1\\
 \to x <  – \dfrac{1}{5}
\end{array}\)