Chapter2 - : Pre-Calculus - Chapter 2A Chapter 2A - Solving...

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© : Pre - Calculus - Chapter 2A Chapter 2A - Solving Equations Introduction and Review of Linear Equations An equation is a statement which relates two or more numbers or algebraic expressions. For example, the equation 2 4 6 is a statement relating the equality of the expression 2 4 with the number 6. This statement is always true. The equation x 3 12 is a statement relating the equality of the expression x 3 with the number 12. This statement may or may not be true depending on what numerical value the variable x is assigned. A solution is a value of the variable which makes the equation true. It can be seen by inspection that x 9 is a solution of the above equation since 9 3 12 To verify that a number is a solution to an equation, replace the variable with that value. If the resulting statement is true, the value is a solution, otherwise, it is not a solution. We will explore methods for solving many different kinds of equations in this section. The simplest kind is the linear equation, which is an equation that can be written in the form ax b 0 This kind of equation is solved by isolating the variable, namely, undoing what has already been done to it. Example : Solve the equation 6 3 x x 4for x . Solution: Begin by moving all the variable expressions to one side of the equation and all the numbers to the other side: 6 3 x x 4 subtract 6 from both sides 3 x 6 6 x 4 6 Note the commutative property 3 x x 10 now subtract x from both sides 3 x x x x 10 x x cancels to 0 2 x 10 divide both sides by 2 x 5 Final solution We can check our solution by replacing x with 5 in the original equation: 6 3 5 5 4? 6 15 9? 9 9 Therefore, our solution is correct. © : Pre - Calculus
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© : Pre - Calculus - Chapter 2A Question : Why does the strategy in the previous example work? Answer: Itiseasytoverifythestrategyforanequationoftheform ax b 0usingthe properties of real numbers: ax b b 0 b ax 0 0 b Additive Inverse Property ax b Identity for Addition 1 a ax 1 a b Multiplying by 1 a is the same as dividing by a 1 x b a Multiplicative Inverse x b a Identity for Multiplication © : Pre - Calculus
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© : Pre - Calculus - Chapter 2A Solving Quadratic Equations A quadratic equation is an equation that can be written in the form ax 2 bx c 0 This is referred to as the standard form of a quadratic equation. We will discuss three methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula.
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This note was uploaded on 02/23/2010 for the course CHEM 107 taught by Professor Generalchemforeng during the Fall '07 term at Texas A&M.

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Chapter2 - : Pre-Calculus - Chapter 2A Chapter 2A - Solving...

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