a: 4x-3=2(x+1)
=>4x-3=2x+2
=>4x-2x=3+2
=>2x=5
=>\(x=\dfrac{5}{2}\)
b: \(\dfrac{x+1}{2}-3=\dfrac{x-2}{4}\)
=>\(\dfrac{2\left(x+1\right)-12}{4}=\dfrac{x-2}{4}\)
=>2x+2-12=x-2
=>2x-10=x-2
=>2x-x=-2+10
=>x=8
c: \(x^2-6x+9=0\)
=>\(\left(x-3\right)^2=0\)
=>x-3=0
=>x=3
d: \(x^2-3x=0\)
=>x(x-3)=0
=>\(\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
e: \(x^4-x^2=0\)
=>\(x^2\left(x^2-1\right)=0\)
=>\(\left[{}\begin{matrix}x^2=0\\x^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x\in\left\{1;-1\right\}\end{matrix}\right.\)
=>\(x\in\left\{0;1;-1\right\}\)
f: \(3x^2+4x-7=0\)
=>\(3x^2-3x+7x-7=0\)
=>3x(x-1)+7(x-1)=0
=>(x-1)(3x+7)=0
=>\(\left[{}\begin{matrix}x-1=0\\3x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{7}{3}\end{matrix}\right.\)
