**Equality**- two equations or quantities are of equal and the same value.

**Inequality**- two equations or quantities are lesser or greater than each other.

**Basic Laws of Equality**

**Reflexive Property: x = x****Symmetric Property: if x = y, then y = x****Transitive Property:****if x = y, and y = z, then, x = z. (x = y = z)****if w = x, and y = z, then, w + y = x + z.****if w = x, and y = z, then, wy = xz.**

**First Conclusion:**things equal to the same thing are equal to each other.**Second Conclusion:**equals added to equals are equals**Third Conclusion:**equals multiplied to equals are equals

**Basic Laws of Inequality**

**x > y; x is greater than y****x < y; x is less than y****x </= y; x is less than or equal to y****x>/=y; x is greater than or equal to y**

**Basic Theorems on Inequalities**

**x > y if and only if -x < -y****if x > 0, then -x < 0****if -x > 0, then x < 0****if x > y, z < 0, then ac < bc****if x > y, w > z, then (x + w) > (y + z)****if x > y, w> z, and w, x, y, z > 0, then xw > yz****if x > 0, y > 0, x > y, then 1/x < 1/y**

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