Assignment 13

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

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15:28:09 `questionNumber 130000 **** query 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.

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RESPONSE --> <----------------------------(======)------------------> -2 -1 0 1 2 0 less than or equal to x less than or equal to 1

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15:30:45 `questionNumber 130000 ** 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. **

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RESPONSE --> opps I forgot about half-closed interval. <---------------[==========)-------------> 0 1

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15:32:48 `questionNumber 130000 **** query 1.5.40 (was 1.5.30). How did you fill in the blank for 'if x < -4 then x + 4 ____ 0'?

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RESPONSE --> if x < -4 then x + 4 _______ 0. if x < -4 then x + 4 < 0

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15:33:04 `questionNumber 130000 ** 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. **

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RESPONSE --> correct

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15:33:58 `questionNumber 130000 **** query 1.5.46 (was 1.5.36). How did you fill in the blank for 'if x > -2 then -4x ____ 8'?

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RESPONSE --> if x > -2 then -4x ______ 8 if x > -2 then -4x = 8

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15:34:53 `questionNumber 130000 **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. **

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RESPONSE --> wrong. But I know what I did. I need to multiply both sides by -4.

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15:37:19 `questionNumber 130000 **** query 1.5.58 (was 1.5.48). Explain how you solved the inquality 2x + 5 >= 1.

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RESPONSE --> 2x + 5 >= 1 2x >= -4 x >= -2 This is true. CHECK: 2(-2) +5 >= 1 -4 + 5 >= 1 1 >= 1

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15:37:27 `questionNumber 130000 ** 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. **

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RESPONSE --> correct

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15:44:39 `questionNumber 130000 **** query 1.5.64 (was 1.5.54). Explain how you solved the inquality 8 - 4(2-x) <= 2x.

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RESPONSE --> 8 - 4(2-x) <= 2x 8 - 8 + 4x <= -2x 4x <= -2x -2x <= x

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15:46:28 `questionNumber 130000 ** 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 **

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RESPONSE --> I was going to go that route and subtract 2x from both sides, but I didn't know if that was correct or not. I guess that teaches me to trust your first instinct.

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15:52:20 `questionNumber 130000 **** query 1.5.76 (was 1.5.66). Explain how you solved the inquality 0 < 1 - 1/3 x < 1.

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RESPONSE --> 0 < 1 - 1/3x < 1 0-1 < 1-1 - 1/3x < 1-1 -1 < -1/3x < 0 -1/-(1/3) < (-1/3)/(-1/3) < 0 / (1/3) 3 < x < 0

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15:52:56 `questionNumber 130000 ** 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. **

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RESPONSE --> I think I got this one correct.

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16:02:27 `questionNumber 130000 **** query 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.

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RESPONSE --> -3 < x < 3 then a < 1 - 2x < b -3x < x < 3 6x < -2x < -6 Multiply each part by -2 7x < 1 - 2x < -5 Add 1 to each part

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16:03:41 `questionNumber 130000 ** 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. **

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RESPONSE --> I got the numbers right, but the inequalities I am mixing up or not changing. When should I change them??

When you multiply or divide by a negative number, the direction of the inequality changes.

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16:40:03 `questionNumber 130000 **** query 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?

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RESPONSE --> p = price c = commission c = $25 + .40(p - 70) = $25 + .40p - 28 = .40p - 3 70 <= p <= 300 .40(70) <= .40p <= .40(300) 28 <= .40p <= 120 28-3 <= .40p - 3 <= 120 - 3 25 <= .40p - 3 <= 117 The commission ranges from $25 to $117. 25 / 70 = .36 = 36% 117 / 300 = .39 = 39% The percent commission ranges from 36% to 39%

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16:41:39 `questionNumber 130000 ** 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. **

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RESPONSE --> I got it wrong from what you wrote as the answer. I worked it from #105 and used the maroon book that came with all my books that has the odd answers worked out. I thought I did this right because I worked it out step for step. What did I do wrong?

The question asked for commission. You had

28 <= .40p <= 120 , which is correct.

The commission is .40 p + 25. Had you added 25 to every expression you would have had

28 + 25 <= .40 p + 25 <= 120 + 25 so 53 <= commission <=145.

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16:45:18 `questionNumber 130000 **** query 1.5.112. Why does the inequality x^2 + 1 < -5 have no solution?

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RESPONSE --> This has no solution because: x^2 + 1 < -5 (x^2)^2 < (-6)^2 x < 36 Check: (36)^2 + 1 < -5 1296 + 1 < -5 1297 < -5 This solution is not true!!!

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16:45:57 `questionNumber 130000 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. **

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RESPONSE --> Correct

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Good work overall. See my notes and let me know if you have questions.