Assign 13

course Mth 158

I plan to take the test next week before the deadline.

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.

013. `* 13

*********************************************

Question: * 1.5.34 (was 1.5.24). How did you write the interval [0, 1) using an inequality with x? Describe your illustration using the number line.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

[0, 1) consisting of all real numbers x for which 0 <= x < 1

To depict this on a number line you would draw a [ at the 0 place and fill in the line to 1 where you would place )

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * My notes here show the half-closed interval [0, 1).

When sketching the graph you would use a filled dot at x = 0 and an unfilled dot at x = 1, and you would fill in the line from x = 0 to x = 1. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

I’m not sure where the filled dot sketch comes from. I didn’t see that in the book. All I saw was the graph using a [ and ) to show which number was <= or <

I believe the way I would draw my graph would be the same as the filled dot.

------------------------------------------------

Self-critique Rating: 3

*********************************************

Question: * 1.5.40 (was 1.5.30). How did you fill in the blank for 'if x < -4 then x + 4 ____ 0'?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

if x < -4 then x + 4 < 0

using the addition property of inequalities that say if a < b the a+c < b+c so by adding 4 to both sides the inequality sign does not change.

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * if x<-4 then x cannot be -4 and x+4 < 0.

Algebraically, adding 4 to both sides of x < -4 gives us x + 4 < 0. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

There are no discrepancies

------------------------------------------------

Self-critique Rating: 3

*********************************************

Question: * 1.5.46 (was 1.5.36). How did you fill in the blank for 'if x > -2 then -4x ____ 8'?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

If x > -2 then -4x < 8 because when you multiply by a negative number the inequality sign reverses.

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * if x> -2 then if we multiply both sides by -4 we get

-4x <8.

Recall that the inequality sign has to reverse if you multiply or divide by a negative quantity. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

There are no discrepancies.

------------------------------------------------

Self-critique Rating: 3

*********************************************

Question: * 1.5.58 (was 1.5.48). Explain how you solved the inquality 2x + 5 >= 1.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

2x + 5 >= 1 first add -5 to both sides

2x >= -5 + 1 the divide by 2

2x >= - 4

x >= -2

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * Starting with

2x+5>= 1 we add -5 to both sides to get

2x>= -4, the divide both sides by 2 to get the solution

x >= -2. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

There were no discrepancies.

------------------------------------------------

Self-critique Rating: 3

*********************************************

Question: * 1.5.64 (was 1.5.54). Explain how you solved the inquality 8 - 4(2-x) <= 2x.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

8 – 4 (2-x) <= 2x first distribute on the left

8 – 8 + 4x <= 2x then add -2x to both sides

4x – 2x <= 0 combine like terms and divide by 2

2x <= )

x <= 0

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * 8- 4(2-x)<= 2x. Using the distributive law:

8-8+4x<= 2x. Simplifying:

4x<=2x. Subtracting 2x from both sides:

2x<= 0

x<=0 **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

There were no discrepancies

------------------------------------------------

Self-critique Rating: 3

*********************************************

Question: * 1.5.76 (was 1.5.66). Explain how you solved the inquality 0 < 1 - 1/3 x < 1.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

0 < 1 – 1/3x < 1 you can solve by doing each side separately.

0 < 1-1/3x 1 -1/3x < 1 add -1 to both sides

-1 < -1/3x -13x < 0 now you can multiply both sides by -3

-3(-1) < -3 (-1/3x) -3(-1/3x) < -3(0) multiplying by a negative reverse inequality sign

3 > x x > 0 re-write to read from left to right of the number line

0 < x < 3

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * Starting with

0<1- 1/3x<1 we can separate this into two inequalities, both of which must hold:

0< 1- 1/3x and 1- 1/3x < 1. Subtracting 1 from both sides we get

-1< -1/3x and -1/3x < 0. We solve these inequalitites separately:

-1 < -1/3 x can be multiplied by -3 to get 3 > x (multiplication by the negative reverses the direction of the inequality)

-1/3 x < 0 can be multiplied by -3 to get x > 0.

So our inequality can be written 3 > x > 0. This is not incorrect but we usually write such inequalities from left to right, as they would be seen on a number line. The same inequality is expressed as

0 < x < 3. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

There are no discrepancies

------------------------------------------------

Self-critique Rating: 3

*********************************************

Question: * 1.5.94 (was 1.5.84). Explain how you found a and b for the conditions 'if -3 < x < 3 then a < 1 - 2x < b.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

If -3 < x < 3 then a < 1-2x < b

2(-3) < 2x < 2(3) multiply by 2

-6 < 2x < 6 add the 1

-6 + 1 < 1 – 2x < 6 + 1

-5 < 1-2x < 7

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * Adding 1 to each expression gives us

1 + 6 > 1 - 2x > 1 - 6, which we simplify to get

7 > 1 - 2x > -5. Writing in the more traditional 'left-toright' order:

-5 < 1 - 2x < 7. **

Your solution wasn't completely rigorous; you sort of 'danced around' the issue of the signs. However it was pretty much on the mark.

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

I don’t know how I solved mine and it came out to the right answer. I tried to follow the book, but somehow it doesn’t look like the right way to do it, even if the answer is the same.

------------------------------------------------

Self-critique Rating: 2

*********************************************

Question: * 1.5.106 (was 1.5.96). Explain how you set up and solved an inequality for the problem. Include your inequality and the reasoning you used to develop the inequality. Problem (note that this statement is for instructor reference; the full statement was in your text) commision $25 + 40% of excess over owner cost; range is $70 to $300 over owner cost. What is range of commission on a sale?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

70 <= 25 + 40% * cost < = 300

I get confused with these types of questions. I don’t really know how to set them up even though the question gives us the general set up.

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * If x = owner cost then

70 < x < 300.

.40 * owner cost is then in the range

.40 * 70 < .40 x < .40 * 300 and $25 + 40% of owner cost is in the range

25 + .40 * 70 < 25 + .40 x < 25 + .40 * 300 or

25 + 28 < 25 + .40 x < 25 + 120 or

53 < 25 + .40 x < 145. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

I see how you solve the problem once it has been laid out, but I still don’t really understand how to set up a problem like this.

You made a good start, but didn't incorporate the given information corresponding to 70 < x < 300.

If you combine your statement with this information, it works out as in the solution.

Give it a try and if you have additional questions, submit your attempt and I'll be glad to advise you further.

------------------------------------------------

Self-critique Rating: 1

*********************************************

Question: * 1.5.123 \ 112. Why does the inequality x^2 + 1 < -5 have no solution?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

x^2 + 1 < -5 add -1 to both sides

x^2 < -4

there is no real number that is the square of a negative number so there is no solution

confidence rating:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

* * STUDENT SOLUTION: x^2 +1 < -5

x^2 < -4

x < sqrt -4

can't take the sqrt of a negative number

INSTRUCTOR COMMENT: Good.

Alternative: As soon as you got to the step x^2 < -4 you could have stated that there is no such x, since a square can't be negative. **

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

There are no discrepancies

Good.

Note that x^2 + 1 < -5 actually rearranges to

x^2 < -6,

not x^2 < -4 as in your solution and in the given solution. The end result is the same--the inequality has no solution because x^2 can't be negative--but let's both be careful about the details.

------------------------------------------------

Self-critique Rating: 3

"

rating: