a) \(-7\cdot\left(x+9\right)-3\cdot\left(5-x\right)=2\\ -7x+\left(-63\right)-15+3x=2\\ \left(-7x+3x\right)+\left[\left(-63\right)-15\right]=2\\ -4x+\left(-78\right)=2\\ -4x=2-\left(-78\right)\\ -4x=2+78\\ -4x=80\\ x=80:\left(-4\right)\\ x=-20\)Vậy x = -20
b) \(\left(x-6\right)\cdot\left(x+5\right)\le0\)
Ta xét 2 TH:
\(\circledast\left(x-6\right)\cdot\left(x+5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x-6=0\\x+5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0+6\\x=0-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6\\x=-5\end{matrix}\right.\)
\(\circledast\left(x-6\right)\cdot\left(x+5\right)< 0\\ \Rightarrow\left[{}\begin{matrix}x-6< 0\\x+5< 0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x< 0+6\\x< 0-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x< 6\\x< -5\end{matrix}\right.\)
Vậy:
+, Nếu (x-6).(x+5)=0 thì x ∈ {6 ; -5}
+, Nếu (x-6).(x+5)<0 thì x<6 hoặc x<-5
