1. When we say a value is a "solution" to an equation, what does it mean? In other words, why can I say = 2, 3 are solutions to 2 6 0 xx = ?

2. If I solved the following rational equation 1 2 41 1 x xx + = + and get an answer of x=1, why then would there actually be no solution to this equation? In other words, I would have to enter DNE (Does Not Exist) in the answer box? 3. Application problems require a student to translate words into numerical values, symbols, or operations. a. What would be the reciprocal of the variable ? b. If the first of two consecutive odd integers is x how would I write the 2nd in terms of x? c. When you see the word " is" in an application problem, what mathematical symbol should that translate to?

4. Write an equation to represent the following problem, then solve the equation algebraically. The sum of the reciprocals of 2 consecutive even integers is 9 40. Find the numbers. a. The equation should be .... b. After solving, my two consecutive even integers are....

5. The difference between the following 2 questions is that in the first one they give you information about a river current which would affect the boat, while in the second they do not mention any outside external force that is affecting the trains. The current of a river is 2 miles per hour. A boat travels to a point 3 miles upstream and back in 2 hours. What is the speed of the boat in still water? Train A has a speed 20 miles per hour greater than that of train B. If train A travels 220 miles in the same times train B travels 180 miles, what are the speeds of the two trains?

a. Why is that piece of information, about there being a current or no mention of an outside force such as a current, important in terms of setting up and solving the equation for each?

b. How would you express the speed of the boat going up stream? (use x for speed)

c. How would you express the speed of the boat going down stream? (use x for speed)

d. How would you express the speed of Train A in terms of Train B? (use x for speed)

e. Which of the two expressions below represent the relationship of the time in the boat problem? Choose A, B or C. Note: represent time in the formula = ( = ) A. =+2 B. + =2 C. =

f. Which of the two expressions below represent the relationship of the time in the train problem? Choose A, B or C. Note: represent time in the formula = ( = ) A. =+20 B. + =20 C. =

g. Pick one of the two problems above to solve. You may do both for extra credit.