\(\left|2x+3\right|+5-\left|-\frac{2}{3}\right|=9\)
\(\left(=\right)\left|2x+3\right|+5-\frac{2}{3}=9\)
\(\left(=\right)\left|2x+3\right|+5=9+\frac{2}{3}\)
\(\left(=\right)\left|2x+3\right|+5=\frac{29}{3}\)
\(\left(=\right)\left|2x+3\right|=\frac{29}{3}-5\)
\(\left(=\right)\left|2x+3\right|=\frac{14}{3}\)
\(\left(=\right)\orbr{\begin{cases}2x+3=\frac{14}{3}\\2x+3=-\frac{14}{3}\end{cases}}\)
\(\left(=\right)\orbr{\begin{cases}2x=\frac{14}{3}-3\\2x=-\frac{14}{3}-3\end{cases}}\)
\(\left(=\right)\orbr{\begin{cases}2x=\frac{5}{3}\\2x=-\frac{23}{3}\end{cases}}\)
\(\left(=\right)\orbr{\begin{cases}x=\frac{5}{3}:2\\x=-\frac{23}{3}:2\end{cases}}\)
\(\left(=\right)\orbr{\begin{cases}x=\frac{5}{6}\\x=-\frac{23}{6}\end{cases}}\)
Vậy \(x\in\left\{\frac{5}{6};-\frac{23}{6}\right\}\)
Trả lời:
\(\left|2x+3\right|+5-\left|-\frac{2}{3}\right|=9\)
\(\Rightarrow\left|2x+3\right|+5-\frac{2}{3}=9\)
\(\Rightarrow\left|2x+3\right|+\frac{13}{3}=9\)
\(\Rightarrow\left|2x+3\right|=\frac{14}{3}\)
\(\Rightarrow\orbr{\begin{cases}2x+3=\frac{14}{3}\\2x+3=-\frac{14}{3}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=\frac{5}{3}\\2x=-\frac{23}{3}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{5}{6}\\x=-\frac{23}{6}\end{cases}}\)
