\(\left|2x+3\right|-4x< 9\)
+ TH1: \(x\ge-\frac{3}{2}.\)
\(\left|2x+3\right|-4x< 9\)
\(\Leftrightarrow2x+3-4x< 9\)
\(\Rightarrow-2x+3< 9\)
\(\Rightarrow-2x< 9-3\)
\(\Rightarrow-2x< 6\)
\(\Rightarrow x>6:\left(-2\right)\)
\(\Rightarrow x>-3\) (1).
+ TH2: \(x< -\frac{3}{2}.\)
\(\left|2x+3\right|-4x< 9\)
\(\Leftrightarrow-2x-3-4x< 9\)
\(\Rightarrow-6x-3< 9\)
\(\Rightarrow-6x< 9+3\)
\(\Rightarrow-6x< 12\)
\(\Rightarrow x>12:\left(-6\right)\)
\(\Rightarrow x>-2\) (2).
Từ (1) và (2) \(\Rightarrow x>-2.\)
Vậy \(x>-2\) thì \(\left|2x+3\right|-4x< 9.\)
Chúc bạn học tốt!
