Lect2 - Solving Equations of Degree 1 (Linear Equations):...

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92.131 Lecture 2 1 of 15 Ronald Brent © 2010 All rights reserved. Solving Equations of Degree 1 (Linear Equations): Definition: The equation 0 = + b x a is called an equation of degree 1. Example: Solve for x : 0 25 5 = x . 25 0 25 25 5 + = + x , Or 25 5 = x . Dividing both sides by 5: 5 25 5 5 = x , giving 5 = x . Easy! Check the answer! Substitute 5 = x back into the original equation. 0 25 5 5 = .
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92.131 Lecture 2 2 of 15 Ronald Brent © 2010 All rights reserved. Example: Solve for x : 0 5 3 4 1 = + x . o r 5 3 4 1 = x . = 5 3 4 4 1 4 x . This gives 5 12 = x . Example: Solve for y : 0 2 9 2 = y . ) 2 9 ( 2 = y or 2 9 2 + = y . 2 2 9 + = y . Or () 1 2 2 9 1 2 2 9 2 2 2 9 2 + = + = + = y .
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92.131 Lecture 2 3 of 15 Ronald Brent © 2010 All rights reserved. Word Problems Example: A piece of wire 76-in. long is bent into the shape of a rectangle that is 2-in. longer than it is wide. What is the area of the rectangle? x + 2 x Since the perimeter is 76 inches we have 76 ) 2 ( 2 2 = + + x x . o r 76 4 2 2 = + + x x which is equivalent to 76 4 4 = + x , or 72 4 = x , which has solution 18 = x inches. The dimensions of the rectangle are 18 by 20 inches,
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92.131 Lecture 2 4 of 15 Ronald Brent © 2010 All rights reserved. so the area is 360 sq. in. Example: Two thousand dollars was invested, partly at 5% annual simple interest and partly at 7%. The total interest earned in the first year was $130. How much was invested at 7%? Let x be the amount of money, in dollars, invested at 7%. The remaining money invested at 5% is x 2000 . The amount of interest earned is 130 ) 2000 ( 100 5 100 7 = + x x . Multiplying by 100 gives 000 , 13 ) 2000 ( 5 7 = + x x which reduces to 000 , 13 5 000 , 10 7 = + x x or 3000 2 = x , and hence 1500 = x dollars is the desired answer.
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92.131 Lecture 2 5 of 15 Ronald Brent © 2010 All rights reserved. Solving Equations of Degree 2 (Quadratic Equations): Definition: The equation 0 2 = + + c x b x a is called an equation of degree 2.
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Lect2 - Solving Equations of Degree 1 (Linear Equations):...

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