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20:52:58 **** 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 --> I am not sure how to type ""greater than equal to"" on one line so I will do it as follows, but that is what I mean. 0 <= x < 1 On the number line, 0 will have a bracket and 1 will have a paren. The area between would be shaded.
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20:53:17 ** 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 --> right
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20:55:19 **** 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 --> you use the rule for the addition property of inequalites which states that if the same number is added to both sides of the inequality, the direction of the inequality remains unchanged. So, if x < 4 then x + 4 < 0
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20:55:56 ** 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 --> right
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20:59:11 **** 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 --> again, using the rules for inequalites, this time a muliplication property which states that if you multiply by a neg. #, the direction of the inequality changes. if x > -2, then -4x < 8
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20:59:45 **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 --> right
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21:01:59 **** 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 subtract 5 f/both sides 2x >= -4 divide by 2 x >= -2 [-2, infin)
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21:02:12 ** 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 --> right
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21:06:04 **** query 1.5.64 (was 1.5.54). Explain how you solved the inquality 8 - 4(2-x) <= 2x.
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RESPONSE --> first distribute thru the paren. 8 - 8 + 4x <= 2x subtract 4x 0 <= - 2x divide by neg 2 and flip sign x <= 0
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21:07:34 ** 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 --> ok, i did mine somewhat differently. your way was quicker.
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21:10:51 **** 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 --> first muliply by 3 to get rid of fraction
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21:15:29 ** 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 did these problems as one combined inequality rather than working them seperately.
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21:18:59 **** 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 --> You first have to muliply -2 to each part to gain -2x in the middle: 6 > -2x > -6 next, add 1 to each part 7 > 1 - 2x > -5 so a = 7 b = -5
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21:19:23 ** 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 --> right
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21:24:10 **** 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 --> The saleperson always earn $25 plus 40% commission over owner cost The least amount to earn commission on is $70 and the most $300. Let C=commission 25 + .40(70) <= C <= 25 + .40(300) 25 + 28 <= C <= 25 +120 53 <= C <= 145 so the range of commission is $53 - $145
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21:25:27 ** 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 --> Yours is slightly different from mine. Is either correct or should I have added the middle term?
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21:28:34 **** query 1.5.112. Why does the inequality x^2 + 1 < -5 have no solution?
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RESPONSE --> because when you subtract 1 from both sides you get x^2 < -6 you cannot take the square root -6 because the square of a real number is never negative.
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21:29:21 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 --> right
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