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Published byBreanna Heather
Modified over 5 years ago
Solving Equations A SolutionA value of the variable that makes the equation a true statement
Equations Example: x + 2 = 5 TRUE if x = 3 FALSE if x = anything else The Solution is x = 3
Special Cases Example: x = x + 1 NEVER TRUE No such number existsCalled a contradiction
Special Cases Example: 2x = x + x ALWAYS TRUE True for any numberCalled an identity
Equivalent Equations Have the same solution Example: x + 2 = 5 x – 1 = 2 x + 4 = 7 All have solution x = 3
Addition Principle Adding (or subtracting) the same number to both sides of an equation does not change its solution.
Addition Principle Example: 6 + x = 8 3+6 + x = 3+8 9 + x = 11Are equivalent equations Both have the same solution
Addition Principle Example: 6 + x = 8 -6 -6 x = 2 x = 2 Equivalent equation that shows the solution
Multiplication PrincipleMultiplying (or dividing) same non-zero number to both sides of an equation does not change its solution.
Multiplication PrincipleExample: 6x = 12 3 • 6x = 3 • 12 18x = 36 Are equivalent equations Both have the same solution
Multiplication PrincipleExample: 6x = 12 6x 6 = 12 6 x = 2 Equivalent equation that shows the solution
Multiplication PrincipleAnother Way:
Using Both Principles Usually best to use Addition Principle first.
Using Both Principles Example: 2x – 3 = 7 First add 3: 2x = 10Then 2: x = 5
Objectives The student will be able to:
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