1) Solve: \((2x \ + \ 2)(3x \ - \ 6) \ > \ 0\)
\(\color{red}{x_1 \ = \ -1, \ x_2 \ = \ 2}\)
Test points: \(\color{red}{x \ = \ -2, \ x \ = \ 0, x \ = \ 3}\)
So, \(\color{red}{⇒ \ x \ < \ -1, \ x \ > \ 2}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ x \ < \ -1, \ x \ > \ 2\}}\)
2) Solve: \((2x \ + \ 6)(3x \ - \ 12) \ < \ 0\)
\(\color{red}{x_1 \ = \ -3, \ x_2 \ = \ 4}\)
Test points: \(\color{red}{x \ = \ -4, \ x \ = \ 0, x \ = \ 5}\)
So, \(\color{red}{⇒ \ -3 \ < \ x \ < \ 4}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ -3 \ < \ x \ < \ 4\}}\)
3) Solve: \((-2x \ + \ 6)(4x \ + \ 4) \ < \ 0\)
\(\color{red}{x_1 \ = \ 3, \ x_2 \ = \ -1}\)
Test points: \(\color{red}{x \ = \ -2, \ x \ = \ 0, x \ = \ 4}\)
So, \(\color{red}{⇒ \ x \ < \ -1, \ x \ > \ 3}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ x \ < \ -1, \ x \ > \ 3\}}\)
4) Solve: \(2x^2 \ - \ 10x \ + \ 8 \ < \ 0\)
\(\color{red}{x_1 \ = \ 1, \ x_2 \ = \ 4}\)
Test points: \(\color{red}{x \ = \ 0, \ x \ = \ 2, x \ = \ 5}\)
So, \(\color{red}{⇒ \ 1 \ < \ x \ < \ 4}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ 1 \ < \ x \ < \ 4\}}\)
5) Solve: \(3x^2 \ + \ 12x \ + \ 9 \ > \ 0\)
\(\color{red}{x_1 \ = \ -1, \ x_2 \ = \ -3}\)
Test points: \(\color{red}{x \ = \ -4, \ x \ = \ -2, x \ = \ 0}\)
So, \(\color{red}{⇒ \ x \ < \ -3, \ x \ > \ 4}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ x \ < \ -3, \ x \ > \ 4\}}\)
6) Solve: \(x^2 \ - \ 1 \ > \ 0\)
\(\color{red}{x_1 \ = \ -1, \ x_2 \ = \ 1}\)
Test points: \(\color{red}{x \ = \ -2, \ x \ = \ 0, x \ = \ 2}\)
So, \(\color{red}{⇒ \ x \ < \ -1, \ x \ > \ 1}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ x \ < \ -1, \ x \ > \ 1\}}\)
7) Solve: \(x^2 \ - \ 4 \ < \ 0\)
\(\color{red}{x_1 \ = \ -2, \ x_2 \ = \ 2}\)
Test points: \(\color{red}{x \ = \ -3, \ x \ = \ 0, x \ = \ 3}\)
So, \(\color{red}{⇒ \ -2 \ < \ x \ < \ 2}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ -2 \ < \ x \ < \ 2\}}\)
8) Solve: \((2x \ + \ 2)(3x \ - \ 6) \ < \ 0\)
\(\color{red}{x_1 \ = \ -1, \ x_2 \ = \ 2}\)
Test points: \(\color{red}{x \ = \ -2, \ x \ = \ 0, x \ = \ 3}\)
So, \(\color{red}{⇒ \ -1 \ < \ x \ < \ 2}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ -1 \ < \ x \ < \ 2\}}\)
9) Solve: \(x^2 \ - \ x \ - \ 12 \ > \ 0\)
\(\color{red}{x_1 \ = \ -3, \ x_2 \ = \ 4}\)
Test points: \(\color{red}{x \ = \ -4, \ x \ = \ 0, x \ = \ 5}\)
So, \(\color{red}{⇒ \ x \ < \ -3, \ x \ > \ 4}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ x \ < \ -3, \ x \ > \ 4\}}\)
10) Solve: \((-x \ - \ 1)(x \ + \ 3) \ > \ 0\)
\(\color{red}{x_1 \ = \ -1, \ x_2 \ = \ -3}\)
Test points: \(\color{red}{x \ = \ -4, \ x \ = \ -2, x \ = \ 0}\)
So, \(\color{red}{⇒ \ -3 \ < \ x \ < \ -1}\) is the solution.
Solution set: \(\color{red}{\{x \ | \ -3 \ < \ x \ < \ -1\}}\)