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Published byLillian Perkins Modified over 5 years ago

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DEFINITIONS

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An equation is a statement that two expressions are equal. Usually contains 1 or more variables A variable is a symbol that represents many different numbers in a set of numbers Examples Equation in one variable, w: 12w = 10 Equation in two variables, x and y: 2x + 3y = 12

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Solution of the equation: Any value of a variable that makes an equation true Example: 12w = 10 Because ( ) satisfies the equation, it is a solution

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To solve equations, the Properties of Equality or the Substitution Property may be used

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For real numbers a, b, and c…

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Reflexive a = a Symmetric If a = b, then b = a

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If a = b and b = c, then a = c

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Addition If a = b, then a + c = b + c Subtraction If a = b, then a – c = b - c

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Multiplication If a = b, then ac = bc Division If a = b, then where c ≠ 0

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If a = b, you may replace a with b in any statement containing a and the resulting statement will still be true

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8x – 2 + 4 6x 2 and 17x 2 5 and 1 Terms: The terms that are added or subtracted in an expression such as 5 + 3x – x – 1 Like Terms: The terms 3x and x are like terms because they contain the same form of the variable x

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An expression is simplified when ALL like terms have been combined and all the parenthesis have been removed. Example: 5 + 3x –x -1 3x – x = 2x 5 – 1 = 4

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