1.tìm các giá trị của x để biểu thức có kết quả âm: a) 2x-3 b) 4-3x c) x mủ 2+5x d) 3(2x+3) (3x-5) 2.tìm các giá trị của x để biểu thức có kết quả dươ

Đáp án:

$\begin{array}{l}
1)a)\\
2x – 3 < 0\\
 \Rightarrow 2x < 3\\
 \Rightarrow x < \dfrac{3}{2}\\
b)4 – 3x < 0\\
 \Rightarrow 3x > 4\\
 \Rightarrow x > \dfrac{4}{3}\\
c){x^2} + 5x < 0\\
 \Rightarrow x\left( {x + 5} \right) < 0\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x < 0\\
x + 5 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x > 0\\
x + 5 < 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x < 0\\
x >  – 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x > 0\\
x <  – 5
\end{array} \right.
\end{array} \right.\\
 \Rightarrow  – 5 < x < 0\\
d)3\left( {2x + 3} \right)\left( {3x – 5} \right) < 0\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
2x + 3 > 0\\
3x – 5 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
2x + 3 < 0\\
3x – 5 > 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x >  – \dfrac{3}{2}\\
x < \dfrac{5}{3}
\end{array} \right.\\
\left\{ \begin{array}{l}
x < \dfrac{{ – 3}}{2}\\
x > \dfrac{5}{3}
\end{array} \right.
\end{array} \right.\\
 \Rightarrow  – \dfrac{3}{2} < x < \dfrac{5}{3}\\
2)a)3x – 5 > 0\\
 \Rightarrow 3x > 5\\
 \Rightarrow x > \dfrac{5}{3}\\
b)1 – 2x > 0\\
 \Rightarrow 2x < 1\\
 \Rightarrow x < \dfrac{1}{2}\\
\text{Vậy}\,x < \dfrac{1}{2}\\
c)2{y^2} – 4y > 0\\
 \Rightarrow 2y\left( {y – 2} \right) > 0\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
y > 0\\
y – 2 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
y < 0\\
y – 2 < 0
\end{array} \right.
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
y > 0\\
y > 2
\end{array} \right.\\
\left\{ \begin{array}{l}
y < 0\\
y < 2
\end{array} \right.
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
y > 2\\
y < 0
\end{array} \right.\\
\text{Vậy}\,y > 2\,\text{hoặc}\,y < 0\\
d)5\left( {2y + 1} \right)\left( {3x – 5} \right) > 0\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
2y + 1 > 0\\
3x – 5 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
2y + 1 < 0\\
3x – 5 < 0
\end{array} \right.
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
y >  – \dfrac{1}{2}\\
x > \dfrac{5}{3}
\end{array} \right.\\
\left\{ \begin{array}{l}
y <  – \dfrac{1}{2}\\
x < \dfrac{5}{3}
\end{array} \right.
\end{array} \right.\\
\text{Vậy}\,y >  – \dfrac{1}{2};x > \dfrac{5}{3}\,\text{hoặc}\,y <  – \dfrac{1}{2};x < \dfrac{5}{3}
\end{array}$