Which reasoning method starts with specific cases and then generalizes?

Find the solution set of $x>-5$ if the replacement set is $\{-2,-\mathrm{1,0},\mathrm{1,2},\mathrm{3,4},\mathrm{5,6},7\}$.

In the following question, an equation is given with a questions mark ($?$) in place of the correct figure on the right-hand side which satisfies the equality. Based on the values on the left-hand side and the symbol of equality given, you have to decide which of the following figures will satisfy the equality and thus come in place of the question mark.

Symbol Stands for

$>$ Greater than
$=$ Equal to
$<$ Lesser than
$\ge$ Either greater than or equal to
$\le$ Either Lesser than or equal to

$-\left[\right(36 ÷141) \times 2.5] < ?$

Find the solution set of $\mathrm{x}>-5$ if the replacement set is $\{-10,-9,-8,-7,-6\}$

A plumber can be paid under two schemes as given below:

$\left(\mathrm{i}\right) ₹ 600$ and $₹ 50$ per hour

$\left(\mathrm{ii}\right) ₹ 170$ per hour

If the job takes $n$ hours, then for what values of $n$ does the scheme $\left(\mathrm{i}\right)$ gives the plumber the better wages?