Inequalities: common information
Non-strict inequality. Solving of inequality or system of simultaneous
inequalities. Main properties of inequalities. Some important inequalities.
|1.||If a , then b > a ; or if a > b, then b
|2.||If a > b, then a + c > b + c ; or if a , then a + c That is, one can add (or subtract) the same value to both sides of inequality.|
|3.||If a > b and c > d, then a + c > b + d . That is, inequalities of the same sense ( with the same sign > or can be added term by term. Note, that inequalities of the same sense cannot be subtracted term by term one from another, because the result can be both correct and incorrect.|
|4.||If a > b and c , then a – c > b – d . Or if a and c > d, then a – c That is, inequalities of the opposite sense can be subtract one from another, and the sign of the resulting inequality is the same as of the minuend inequality.|
|5.||If a > b and m > 0, then ma > mb and a/m > b/m . That is, both sides of any inequality can be multiplied or divided by the same positive number; the inequality sense is the same.||6.||If a > b and m , then ma and a/m That is, both sides of any inequality can be multiplied or divided by the same negative number, but the inequality sense changes to the opposite one.|