Amsco Integrated Algebra I: Properties of Inequalities
 This is a free lesson from our course in Amsco's Integrated Algebra

 In this lesson you’ll learn further to earlier learning of definition of the inequality relations >, <, ≥, ≤ in terms of notion of equality, about various properties of inequalities. For the real numbers x, y, and z: If x and y are two real numbers, then one and only one of the following can be true: x < y or x = y or x > y. This illustrates the order property of real numbers.The important properties of inequalities are, • transitive property-For the real numbers x, y & z: if x < y and y < z then x < z; and if z >y and y>x then z>x. • addition property-For the real numbers x, y & z: if x < y , then x+z < y+z; and if x > y, then x+z>y+z. • subtraction property-For the real numbers x, y & z: if x < y then x-z < y-z; and if x>y, then x-z>y-z. (More text below video...)
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 (Continued from above) • multiplication property:-For the real numbers x,y & z:      (i) If z is positive (z>0) and x < y then, xz < yz.      (ii) If z is positive (z>0) and x > y then, xz > yz.      (iii)If z is negative (z<0) and x < y then , x z > yz.      (iv)If z is negative (z<0) and x>y then, xz < yz. The video above will explain in detail with the help of several examples.

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