Jacob

These are the rules for solving linear in-equations.

Suppose M, M₁, N, N₁ 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 M₁> N₁ 

So M + P > N + P and

M₁ + P >N₁+ P

Rule 2: Subtraction Rule

            If M < N and M1 ≥N1

So M - P < N - P and

M₁ - P ≥N₁- P

Rule 3: Multiplication rule

If M ≥N and M₁ > N₁ and P≠ 0

So MP ≥NP; M₁P > N₁P

M(-P) ≤ N(-P) and M₁(-P)  < N₁(-P)

Rule 4: Division

If M > N and M₁< N₁ and  P≠ 0

So M/P > N/P:  M₁/P < N₁/P

M/(-P) < N/(-P) : and M₁/(-P) > N₁/(-P)

Rule 5: Inversion Rule

If M/P ≤ N/Q where P, Q ≠ 0

M₁/P > N₁/Q

So P/M ≥ Q/N and P/M₁ < Q/N₁

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.