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7 Cards in this Set
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Your math teacher has asked you to help her correct some work. Here is the inequality and the solution you have to correct.
Inequality: 5/18 - (x-2)/9 <* (x-4)/6 Student Solution: 5/18 - (x-2)/9 <* (x-4)/6 5/18 - (2/2)(x-2/9)<*(3/3)(x-4/6) 5/18 - 2x-12/18 <* 3x-4/18 5-(2x-2)<* 3x-4 5-2x+2 <* 3x-4 7-2x <* 3x-4 -5x<* -11 x<*11/5 There are two mathematical errors. The first mathematical error occured going from line _____ to line ___ and is incorrect because _______. |
The first mathematical error occured going from line 2 to line 3 and is incorrect because the distributive property was not used correctly. The second term should be 2x-4/18 and the term on the right hand side of the inequality sign should be 3x-12/18.
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Student Solution:
5/18 - (x-2)/9 <* (x-4)/6 5/18 - (2/2)(x-2/9)<*(3/3)(x-4/6) 5/18 - 2x-12/18 <* 3x-4/18 5-(2x-2)<* 3x-4 5-2x+2 <* 3x-4 7-2x <* 3x-4 -5x<* -11 x<*11/5 There are two mathematical errors. The second mathematical error occured going from line _____ to line ___ and is incorrect because _______. |
The second mathematical error occured going from line 7 to 8 and is incorrect because the student divided both sides of the inequality by -5, but did not reverse the direction the inequatlity sign faces, as you always should when dividing by a negative number.
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Student Solution:
5/18 - (x-2)/9 <* (x-4)/6 5/18 - (2/2)(x-2/9)<*(3/3)(x-4/6) 5/18 - 2x-12/18 <* 3x-4/18 5-(2x-2)<* 3x-4 5-2x+2 <* 3x-4 7-2x <* 3x-4 -5x<* -11 x<*11/5 What would you tell the student to help them understand their mistakes? |
Student responses should include explainations of the distributive property and point out that the mistake was that the distributive property was not carried out on all terms for the first mistake, and for the second mistake, student responses should show at least 2 examples of why, when dividing by a negative number, the inequality sign must be flipped.
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Your math teacher has asked you to help her correct some work. Here is the inequality and the solution you have to correct.
Inequality: 5/18 - (x-2)/9 <* (x-4)/6 Now that you have found the student's errors, solve the inequality correctly. |
5/18 - x-2/9 <* x-4/6
5/18 - (2/2)(x-2/9)<*(3/3)(x-4/6) 5/18 - 2x-4/18 <* 3x-12/18 5-(2x-4)<*3x-12 5-2x-4<*3x-12 9-2x<*3x-12 -5x<*-21 5x<*21 x<*21/5 |
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Explain, in words, the steps to solving this equation for x: 3x+7/5=42
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First, multiply both sides of the equation by 5, so you are left with 3x+7=210. Next, subtract 7 from each side so you are left with 3x=203. Finally, divide both sides othe equation to find that x= 67 2/3.
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Why is the first step in solving for x multiplying both sides of the equation by 5 in the example (3x+7)/5=42?
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In order to isolate x, it is necessary to "undo" all of the operations that have been done to it. This must be done in reverse order of operations, and in the case of (3x+7)/5=42, division is the first operation in reverse order.
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Solve. Explain and validate each step. 4(√6x)=20
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Given 4(√6x)=20, the first step is to divide both sides of the equation by 4. The = shows that both sides of the equation are balanced, so whatever is done to one side must also be done to the other. After dividing both sides by 4, you are left with √6x=5. In order to "undo" a square root, the quantity must be squared, or raised to the second power. Since this must be done to the left side, it also must be done to the right. After performing this operation, you are left with 6x=25. Finally, in order to isolate x, 6x must be divided by 6. Since the left side is divided by 6, then the right side must also be divided by 6. This leaves you with x=25/6 or x=4.167
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