rules for solving linear in-equations - linear algebra, Mathematics

Explain what are the Rules for solving linear in-equations?

Posted Date: 2/12/2013 2:45:40 AM | Location : United States





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> N

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.

Posted by Jacob | Posted Date: 2/12/2013 2:47:29 AM


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