 # 1.6. DEFINITIONS  An equation is a statement that two expressions are equal.  Usually contains 1 or more variables  A variable is a symbol that represents.

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1.6

DEFINITIONS

 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

 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

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

For real numbers a, b, and c…

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

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

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

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

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

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

 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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