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Inequalities
An algebraic inequality is a mathematical statement comparing
two unequal algebraic expressions. It states that one algebraic expression
is greater than (>), less than (<), greater than or equal
to (³), or less than or equal to (£), another algebraic expression.
The following additive and multiplicative properties apply to
inequalities.
Addition Property of Inequality:
For all real numbers a, b, and c,
a > b if and only if a + c > b + c.
Multiplication Property of Inequality:
For all real numbers a, b, and c, where c
¹ 0,
(1) If c > 0, then a > b if and only if ac > bc.
(2) If c < 0, then a > b if and only if ac < bc.
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