mac1140_lecture7_1

mac1140_lecture7_1 - L7 2.1 Linear Equations Types of...

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54 L7 §2.1 Linear Equations Types of Equations Identity : An equation satisfied by every number that is a meaningful replacement for the variable. Example : 32 125 ( 5)( 5 25) xx x x −= + + . Conditional equations : Equations satisfied by some numbers but not by others. Example : 2( 5) 3 x x += . Contradiction : An equation that is false for every value of the variable. Example : 3( 3) 3 3 x x + . Such an equation has solution set (empty). This happens whenever you solve and get a ridiculous statement (see the example above). Definition . Equations with the same solution set are called equivalent equations .
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55 Linear Equations Definition . An equation of the form 0 ax b + = , where 0 a , is called a linear equation. Solving Linear Equations : Simplify both sides as much as possible. Get terms with variable on one side and numbers on the other. Simplify and solve for the variable. Example . Solve: 3(3 2 ) 33 2 x x =− Solving equations involving rational expressions : 1. Multiply each term in the equation by the LCD of all fractions and write down restrictions on the variable.
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mac1140_lecture7_1 - L7 2.1 Linear Equations Types of...

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