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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 4 for 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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