These are the rules for solving linear in-equations.
Suppose M, M_{1}, N, N_{1} and P are expressions such may or may not include variables after that the corresponding rules for solving in-equations will be as:
Rule 1: Addition rule
If M > N and M_{1}> N_{1 }
So M + P > N + P and
M_{1} + P >N_{1}+ P
Rule 2: Subtraction Rule
If M < N and M1 ≥N1
So M - P < N - P and
M_{1} - P ≥N_{1}- P
Rule 3: Multiplication rule
If M ≥N and M_{1} > N_{1} and P≠ 0
So MP ≥NP; M_{1}P > N_{1}P
M(-P) ≤ N(-P) and M_{1}(-P) < N_{1}(-P)
Rule 4: Division
If M > N and M_{1}< N_{1} and P≠ 0
So M/P > N/P: M_{1}/P < N_{1}/P
M/(-P) < N/(-P) : and M_{1}/(-P) > N_{1}/(-P)
Rule 5: Inversion Rule
If M/P ≤ N/Q where P, Q ≠ 0
M_{1}/P > N_{1}/Q
So P/M ≥ Q/N and P/M_{1} < Q/N_{1}
Note: The rules for solving equations are the similar as those for solving equations along with one exception; whereas both sides of an equation is divided or multiplied by a negative number, the inequality symbol should be reversed see rule 3 & Rule 4 above.