analyzing equations and inequalities

Before analyzing equations and inequalities first of all it is necessary to know about the equation and inequality. As we know that if equal sign is present in an expression then it is said to be equation. If less than, greater than, less than equal to and greater than equal to operator is present in an expression then it is said to be an inequality. We have to focus on some points to analyzing equation and inequality. Now first of all we will see the properties of equation or (Real number). (know more about Inequality, here)

	Addition	Multiplication
Commutative	P + q = q + p	pq = qp
Associative	(p + q) + r = p + (q + r)	(pq) r = p (qr)
Identity	P + 0 = p = 0 + p	p (1) = p = 1 (p)
Inverse	P + (-p) = 0 = (-p) + p	If p ≠0 then p (1/p) = 1 = 1/p(p)

If we talk about the inequality property then we can write the properties as: For any two real number p and q, one of the given statements is true. p < q, p = q, p > q

Addition and subtraction properties for inequality	For any real numbers p, q and r: 1.      If p > q then p + r > q + r and p – r > q – r 2.      If p < q then p + r < q + r and p – r < q – r
Multiplication and Division property of inequality	For any real number p, q and r: 1.      If  r is positive and p < q then pr < qr and p/r < q/r 2.      If  r is positive and p > q then pr > qr and p/r > q/r 3.      If  r is negative and p < q then pr > qr and p/r > q/r 4.      If  r is positive and p > q then pr < qr and p/r < q/r

If we apply these properties then we can easily analysis the equation and inequality. VSEPR Theory is based on chemistry. The icse guess papers 2013 are useful for the preparation of exam.