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 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...)
<h2>Properties of Inequalities</h2> <p>math, algebra,inequalities,Properties of Inequalities,math,Transitive Property of Inequality,Subtraction Property of Inequality,Multiplication Property of Inequality, video</p> <p> explains about various properties of inequalities.</p>
People who saw this lesson also found the following lessons useful:
Solving Equations Using More Than One Operation
Solving Equations That Have the Variable in Both Sides
Solving for a Variable in Terms of Another Variable
Using Inequalities to Solve Problems
(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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