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14:52:36 `q001. Explain the difference between x - 2 / x + 4 and (x - 2) / (x + 4). The evaluate each expression for x = 2.
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RESPONSE --> x - 2 / x + 4 requires dividing 2 by x, subtracting that result from x, and then adding 4. (x - 2) / (x + 4) requires subtacting 2 from x and adding 4 to x, then dividing the first result (x-2) by the second result (X+4). If x=2, x - 2 / x +4 = 2 - 2/2 + 4 = 5 If x=2, (x - 2) / (x + 4) = (2-2)/(2+4) = 0/6 = 0 confidence assessment: 3
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15:21:13 `q003. What is the numerator of the fraction in the expression x - 3 / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x? What is the denominator? What do you get when you evaluate the expression for x = 2?
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RESPONSE --> The numerator is x - 3. The denominator is [(2x - 5)^2 * 3x + 1]. If x = 2, the value of the expression is 11 6/7. 2-3/[(2*2-5)^2*3*2+1] -2 +(7*2) = -1/[(-1^2)*6+1] -2 +14 = -1/[1*6+1] +12 = -1/7 + 12 = 11 6/7 confidence assessment: 3
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15:30:59 The numerator is 3. x isn't part of the fraction. / indicates division, which must always precede subtraction. Only the 3 is divided by [ (2x-5)^2 * 3x + 1 ] and only [ (2x-5)^2 * 3x + 1 ] divides 3. If we mean (x - 3) / [ (2x-5)^2 * 3x + 1 ] - 2 + 7x we have to write it that way. The preceding comments show that the denominator is [ (2x-5)^2 * 3x + 1 ] Evaluating the expression for x = 2: - 3 / [ (2 * 2 - 5)^2 * 3(2) + 1 ] - 2 + 7*2 = 2 - 3 / [ (4 - 5)^2 * 6 + 1 ] - 2 + 14 = evaluate in parenthese; do multiplications outside parentheses 2 - 3 / [ (-1)^2 * 6 + 1 ] -2 + 14 = add inside parentheses 2 - 3 / [ 1 * 6 + 1 ] - 2 + 14 = exponentiate in bracketed term; 2 - 3 / 7 - 2 + 14 = evaluate in brackets 13 4/7 or 95/7 or about 13.57 add and subtract in order. The details of the calculation 2 - 3 / 7 - 2 + 14: Since multiplication precedes addition or subtraction the 3/7 must be done first, making 3/7 a fraction. Changing the order of the terms we have 2 - 2 + 14 - 3 / 7 = 14 - 3/7 = 98/7 - 3/7 = 95/7. COMMON STUDENT QUESTION: ok, I dont understand why x isnt part of the fraction? And I dont understand why only the brackets are divided by 3..why not the rest of the equation? INSTRUCTOR RESPONSE: Different situations give us different algebraic expressions; the situation dictates the form of the expression. If the above expression was was written otherwise it would be a completely different expression and most likely give you a different result when you substitute. If we intended the numerator to be x - 3 then the expression would be written (x - 3) / [(2x-5)^2 * 3x + 1 ] - 2 + 7x, with the x - 3 grouped. If we intended the numerator to be the entire expression after the / the expression would be written x - 3 / [(2x-5)^2 * 3x + 1 - 2 + 7x ].
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RESPONSE --> I understand my mistake. I included the x in the numerator. Careless mistake--I understand the order of operations and need to be more careful. 2 - 3/[(2*2-5)^2*3*2+1] -2 +14 = 2 - 3/(4-5)^2*6+1] -2 +14 = -3/[1*6+1] +14 = -3/7 +14 = 13 4/7 or 95/7 Question: How much work do you want to be shown in the response? self critique assessment: 2
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15:43:42 `q004. Explain, step by step, how you evaluate the expression (x - 5) ^ 2x-1 + 3 / x-2 for x = 4.
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RESPONSE --> substitute 4 for x: (4-5)^2*4 -1 +3/4 -2 perform subtraction inside parentheses: -1^2*4 -1 +3/4 -2 square -1: 1*4 -1 +3/4 -2 multiply: 4 -1 +3/4 -2 add & subtract: 1 3/4 confidence assessment: 2
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15:49:17 *&*& Standard mathematics notation is easier to see. On the other hand it's very important to understand order of operations, and students do get used to this way of doing it. You should of course write everything out in standard notation when you work it on paper. It is likely that you will at some point use a computer algebra system, and when you do you will have to enter expressions through a typewriter, so it is well worth the trouble to get used to this notation. Indicate your understanding of the necessity to understand this notation.
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RESPONSE --> I understand the need to understand the notation required by computer algebra programs, since they are limited to the entries possible with a keyboard. self critique assessment: 3
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