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Unformatted text preview: Name: Econ 1078.004 – ANSWER KEY Spring 2008 In-Class Assignment 1 (10 Points) February 6, 2008 Show Your Work! 1. Simplify the following by rationalizing the denominator: 3 5 ) 1 (-- x 22 3 5 3 5 3 3 5 3 5 25 3 5 3 5 ) 3 5 ( ) 3 5 ( ) 3 5 ( ) 1 (-- + =-- +-- + = + +-- x x x x x 2. Find the values of x that satisfy: ) 1 ( 3 2 5 4 ) 2 ( 15 8- < + +- x x x x The common denominator here is 15, so we have: x x x x x x x x x x x x x x x x <- <-- <-- < +--- < + +-- < + +- 4 5 20 10 10 30 5 10 10 12 30 15 8 )) 1 ( 2 ( 5 ) 4 ( 3 ) 2 ( 15 8 ) 1 ( 3 2 5 4 ) 2 ( 15 8 3. Solve the following inequalities: (a). ) 3 ( ) 1 ( ≤ +- x x This problem is already simplified, and we can see that the critical points are 1 and –3. So then we test numbers around these: Test (-4): 1 5 ≤- which is true Test: (0): 3 1 ≤ which is false Test: (2): 5 1 ≤- which is true So the answer is 3- < x or 1 ≥ x (b)....
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