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

Before searching at series solutions to a differential equation we will initially require to do a cursory review of power series. So, a power series is a series in the form, .

Triangles, In a triangle ABC, D &E is a are points on AB & AC ,if the one s...

In a triangle ABC, D &E is a are points on AB & AC ,if the one side of a triangle is 4cm & another side is 5 cm find that the ar(triangleABC):ar(BCDE)

Jacob 2/12/2013 2:47:29 AM 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.

Jacob

2/12/2013 2:47:29 AM

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.

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