Scalene: means 'uneven' or 'odd', so no equal sides. For example: $$|x - 3| ≤ 9 ⇔ -9 < x - 3 < 9$$ $$⇔ -6 < x < 12$$įrom: en.wikipedia. How to remember Alphabetically they go 3, 2, none: Equilateral: 'equal'-lateral (lateral means side) so they have all equal sides Isosceles: means 'equal legs', and we have two legs, rightAlso iSOSceles has two equal 'Sides' joined by an 'Odd' side. These relations may be used to solve inequalities involving absolute values. Two other useful properties concerning inequalities are: $$|a| ≤ b ⇔ -b ≤ a ≤ b$$ $$|a| ≥ b ⇔ a ≤ -b \space or \space b ≤ a$$ Idempotence (the absolute value of the absolute value is the absolute value) $$||a|| = |a|$$ Symmetry $$|-a| = |a|$$ Identity of indiscernibles (equivalent to positive-definiteness) $$|a - b| = 0 ⇔ a = b$$ Triangle inequality (equivalent to subadditivity) $$|a - b| ≤ |a - c| |c - b|$$ Preservation of division (equivalent to multiplicativeness) $$|a / b| = |a| / |b| \space\space if \space\space b ≠ 0$$ (equivalent to subadditivity) $$|a - b| ≥ ||a| - |b||$$ Other important properties of the absolute value include: (2) : identical in mathematical value or logical denotation : equivalent. Non-negativity $$|a| ≥ 0$$ Positive-definiteness $$|a| = 0 ⇔ a = 0$$ Multiplicativeness $$|ab| = |a||b|$$ Subadditivity $$|a b| ≤ |a| |b|$$ a (1) : of the same measure, quantity, amount, or number as another. cognitive limitations in developing a relational meaning of the equal sign. The absolute value has the following four fundamental properties: As algebra has taken a more prominent role in mathematics education, many are. Furthermore, the absolute value of the difference of two real numbers is the distance between them. Form of a Quadratic Equation The Standard Form for writing down a Quadratic Equation is ( a not equal to zero) Example: Put. The absolute value of a number may be thought of as its distance from zero along real number line. The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign.įor example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. Browse the definitions using the letters below, or use Search above. Solve the Quadratic Equation by the Quadratic Formula Easy-to-understand definitions, with illustrations and links to further reading.Solve the Quadratic Equation by Factoring.a b, means, a b or a > b, but vice-versa does not hold true. This property states that adding the same amount to both members of an equation preserves the equality. x y, means, y x or y > x, but not vice-versa. ![]() Also, an example is provided to understand the usage of mathematical symbols. Solve the Quadratic Equation by Extracting Roots Here is a list of commonly used mathematical symbols with names and meanings.The symbol for equal is, which we use to separate the two sides of equations. For example, if you and your friend both bring 2 packets of chips on a trip, you brought an equal number of things. Multiplying and Dividing Positive and Negative Whole Numbers In mathematics, the term equal means that two or more values or expressions are the same.
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