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Inequalities


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Graph of an Inequality
Graph that shows all the solutions of the inequality
Addition Property of Inequality
Given x, y, and z are real numbers If x < y, then x + z < y + z
equivalent inequalities
Inequalities that have the same solutions
Subtraction Property of Inequality
Given x, y, and z are real numbers If x < y then x - z < y - z
inequality
A mathematical sentence that shows the relationship between quantities that are not equivalent
Multiplication Property of Inequality
Given x, y, and z are real numbers
Division Property of Inequality
Given x, y, and z are real numbers
compound inequality
Two separate inequalities joined by AND or OR.
intersection
The graph of a compound inequality with "and" in which the solution is the overlapping or what is shared.
union
The graph of a compound inequality with "or" in which the solution is all points that satisfy one or the other or both inequalities.
Absolute value equation
An equation that contains an absolute value expression
Absolute Deviation
The absolute value of the difference of x and the given value
No Solution
If an inquality is equivalent to an inequality that is false, such as 4 < -2.
All Real Numbers
If an inquality is equivalent to an inequality that is true, such as -4 < 2.
absolute value
The distance of a number from zero on a number line; shown by | |
pos x pos = positive
multiplication and division of signed numbers
inverse operations
operations that undo each other
Undefined
when dividing a nonzero number by zero,
indeterminate
zero divided by zero,
commutative property for multiplication
the order in which two real numbers are multiplied does not effect the product. For example,
reciprocal / multiplicative inverse
one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2
order of operations
The rules for calculating a maths question containing mixed operations, such as 14 - 2 x 4 + 12
symbols of inclusion
Symbols that are used to set apart portions of an expression so that they may be evaluated first: ( ), [ ], { }, and the division bar in a fraction.