course MTH 158 œ×„–×x‡P¢|²±ñ¢ï€˜ê„¬assignment #013 013. `query 13 College Algebra 06-23-2008
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10:05:04 **** 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 --> --[0--------------------1) How am I supposed to shade where x is using a keyboard?? confidence assessment: 3
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10:05:54 ** 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 --> How do I type a filled dot? self critique assessment: 2
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10:08:41 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 confidence assessment: 3
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10:08:59 ** 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 --> ok self critique assessment: 3
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10:14:17 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 because I multiplied both sides by -2, which changed the direction of the inequality. confidence assessment: 3
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10:14:26 **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 --> ok self critique assessment: 3
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10:22:28 1.5.58 (was 1.5.48). Explain how you solved the inquality 2x + 5 >= 1.
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RESPONSE --> In my book the question is 2x + 5 > 1. However, I am assuming that 2x + 5 >=1 means that 5 is larger than or equal to 1, so I'll solve for that instead of what my book says. 2x + 5 >= 1 - 5 -5 = 2x >= -4 2x / 2 >= -4 / 2 x >= -2 {x | x >= -2} confidence assessment: 2
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10:22:34 ** 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 --> ok self critique assessment: 3
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10:39:04 1.5.64 (was 1.5.54). Explain how you solved the inquality 8 - 4(2-x) <= 2x.
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RESPONSE --> Distribute... 16 - 8x - 8 + 4x <= 2x 8 - 4x <= 2x -8 - 2x -2x -8 -6x <= -8 x >= 4/3 confidence assessment: 3
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10:40:19 ** 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 --> Oops - I see that I multiplied 8-4 times 2-x rather than just 4 times 2-x. I guess I'm still in the FOIL mode... self critique assessment: 2
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10:46:11 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 - 1/3 x < 1 -1 -1 -1 -1 < -1/3x < 0 multiplying by 3 -3 < -x < 0 dividing by -1 {x | 3 > x > 0 } confidence assessment: 3
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10:46:27 ** 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 --> ok self critique assessment: 3
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10:54:23 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 --> Multiply each term in the first by -2 (-2)-3 < (-2)x < (-2)3 6 > -2x > -6 then add 1 to each term 7 > 1-2x > -5 a = 7, b = -5 confidence assessment: 3
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10:54:37 ** 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 --> ok self critique assessment: 3
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11:52:08 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 commission equation would be c = 25 + .4x, x representing the selling price excess to the owner's cost. Range of commission would be C = 25 + .4(70) and C = 25+.4(300) 25 + .4(70) <= C <= 25 + .4 (300) 53 <= c <= 145 confidence assessment: 2
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11:53:09 ** 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 --> understood self critique assessment: 2
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11:55:06 1.5.122. Why does the inequality x^2 + 1 < -5 have no solution?
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RESPONSE --> x^2 + 1 < -5 -1 -1 x^2 < -6 No solution because you can't have a square root of a negative number. confidence assessment: 2
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11:55:20 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 --> ok self critique assessment: 3
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