If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution:

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

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Question: *   R.1.26 \ was R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?

Your solution:

Confidence Assessment:

Given Solution:

* * ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers

Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers.

Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. **

Self-critique (if necessary):

Self-critique Rating:

Question:  *   R.1.44 \ 32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6

Your solution:

Confidence Assessment:

Given Solution:

* * ** The product of 2 and x is 2 * x and the product of 4 and 6 is 4 * 6. To say that these are identical is to say that 2*x=4*6. **

Self-critique (if necessary):

Self-critique Rating:

Question: 

*   R.1.62 \ 50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]

Your solution:

Confidence Assessment:

Given Solution:

* *  **Starting with

2-5*4-[6*(3-4)]. First you evaluate the innermost group to get

2-5*4-[6*-1] . Then multiply inside brackets to get

2-5*4+6. Then do the multiplication to get

2-20+6. Then add and subtract in order, obtaining

-12. **

Question:  *   R.1.98 \ 80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4).

Your solution:

Confidence Assessment:

Given Solution:

* * ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL.

Starting with

(x-2)(x-4) ; one application of the Distributive Property gives you

x(x-4) - 2(x-4) . Applying the property to both of the other terms we get

x^2 - 4x - (2x -8). Simplifying:

x^2 - 4x - 2x + 8 or

x^2 - 6x + 8. *

Self-critique (if necessary):

Self-critique Rating:

Question: 

*   R.1.102 \ 86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.

Your solution:

Confidence Assessment:

Given Solution:

* * ** Good answer but at an even more fundamental level it comes down to order of operations:

(4+3)/(2+5) means

7/7 which is equal to

1.

By order of operations, in which multiplications and divisions precede additions and subtractions,

4/2+3/5 means

(4/2) + (3/5), which gives us

2+3/5 = 2 3/5

*   Add comments on any surprises or insights you experienced as a result of this assignment.