course Mth 158 I have sent assignments 11&12 on the 15th and 16th, but have gotten no response. Did you receive them?
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09:16:17 **** 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_< x<1 My number line started with [ on 0 and ended with ) at the 1.
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09:17:13 ** 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 --> ok
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09:17:25 **** 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 --> <
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09:17:47 ** 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
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09:18:14 **** 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 --> <
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09:18:25 **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
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09:20:52 **** 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 > 1 - 5 2x > -4 x > -2 (-2, Infin)
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09:21:01 ** 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
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09:23:28 **** 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 0 <= -6x
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09:24:35 ** 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 --> The 2x was a negative.
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09:26:51 **** 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 --> 0 < 1 - 1/3x <1 Myltiplied by 3 0 < 3 -x < 3 subtracted 3 -3 < -x < 0 divided by -1 3> x> 0
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09:37:13 **** 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(-2) < -2x < 3(-2) 6> -2x> -6 6 + 1 > 1- 2x > -6 + 1 7 > 1 - 2x > -5 -5 < 1-2x < 7 a= -5 b = 7
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09:37:41 ** 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
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09:39:23 **** 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 --> I have trouble with word problems. I attempted it and came up with 105<= c <= 1225
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09:40:47 ** 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 have no idea where the 70 came from.
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09:42:20 **** query 1.5.123 \ 112. Why does the inequality x^2 + 1 < -5 have no solution?
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RESPONSE --> Any time a number is squared, it is positive. Adding a positive 1 still makes it positive. Any number substitued for x cannot be < a negative number.
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09:42:37 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
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