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# ws01 - WORKSHEET 1 1 Below is a list of some simple algebra...

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WORKSHEET 1 1. Below is a list of some “simple” algebra problems. Some of the solutions are correct and some of them are wrong ! For each problem: A. determine if the answer is correct; B. determine if there are any mistakes made in solving the problem and list them ( note that just because the answer is corrrect does not mean there are no mistakes); C. if there are mistakes, redo the problem correctly; if there are no mistakes, devise ANOTHER correct method to solve the problem. a) x 2 1 x + 1 = x 2 + ( 1) x + 1 = x 2 x + 1 1 = x 1 b) ( x + y ) 2 ( x y ) 2 = x 2 + y 2 x 2 y 2 = 0 c) 9( x 4) 2 3 x 12 = 3 2 ( x 4)2 3 x 12 = (3 x 12) 2 3 x 12 = 3 x 12 d) x 2 y 5 2 x 3 = x 2 y 5 · 2 x 3 = 2 x 6 y 5 e) (2 x 3 + 7 x 2 + 6) (2 x 3 3 x 2 17 x + 3) ( x + 8) + ( x 8) = (2 x ) 2 17 x + 9 2 x = 2 x 17 x + 9 = 15 x + 9 = 6 x f) x 1 + y 1 x 1 y 1 = ( x + y ) 1 ( x y ) 1 = x + y x y 1 = x + y x y = x + y y x 2. Solve the following inequalities. Whenever possible, use distance arguments.
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