Question

Answer 1

a. (2x - 6)(4x + 16) = 0

\(\Leftrightarrow\left[{}\begin{matrix}2x-6=0\\4x+16=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\) 

S = \(\left\{3,-4\right\}\) 

d. (2x + 4)(3x + \(\dfrac{1}{3}\) ) = 0

\(\Leftrightarrow\left[{}\begin{matrix}2x+4=0\\3x+\dfrac{1}{3}=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{-1}{9}\end{matrix}\right.\) 

S = \(\left\{-2,\dfrac{-1}{9}\right\}\) 

b. (x + 1)(5x - 20) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\5x-20=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-4\end{matrix}\right.\) 

S = \(\left\{-1,-4\right\}\) 

c. (5 - 3x)(2x + 6) = 0

\(\Leftrightarrow\left[{}\begin{matrix}5-3x=0\\2x+6=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-3\end{matrix}\right.\) 

S = \(\left\{\dfrac{5}{3},-3\right\}\) 

e. (x + 3) + x² - 9 = 0

\(\Leftrightarrow\) (x + 3) + (x + 3)(x - 3) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x-3=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=3\end{matrix}\right.\) 

S = \(\left\{-3,3\right\}\) 

f. x(4x - 7)(\(\dfrac{3}{4}\) x - 3) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\4x-7=0\\\dfrac{3}{4}x-3=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{7}{4}\\x=4\end{matrix}\right.\) 

S = \(\left\{0,\dfrac{7}{4},4\right\}\) 

g. x² + 5x + 4 = 0

\(\Leftrightarrow x^2+x+4x+4=0\) 

\(\Leftrightarrow\left(x^2+x\right)+\left(4x+4\right)=0\)

\(\Leftrightarrow x\left(x+1\right)+4\left(x+1\right)=0\) 

\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+4=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-4\end{matrix}\right.\) 

S = \(\left\{-1,-4\right\}\)