For the following equations, decide if the equation has a unique solution, no solution, or infinitely many solutions. You need to get all answers correct before obtaining credit.

? unique solution no solution infinitely many solutions 1. $2 x + 2 = 2 x + 7$

? unique solution no solution infinitely many solutions 2. $2 x + 7 = 2$

? unique solution no solution infinitely many solutions 3. $\frac{1}{2 x + 7} = \frac{2}{2 x + 7}$

? unique solution no solution infinitely many solutions 4. $\frac{1}{2 x + 7} = \frac{1}{7 x + 2}$

? unique solution no solution infinitely many solutions 5. $2(2 x + 7) = 4 x + 14$

? unique solution no solution infinitely many solutions 6. $(x+2)(x+7) = x^2 + 9 x + 14$

Hint: Study the definition and discussion of 'linear equation'.