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Math Help - This question doesn't make any sense to me

  1. #1
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    This question doesn't make any sense to me

    Whats up people. I'm in Trig/PreCalc in school but I just moved to the United States a couple months ago so I never fully studied absolute value, since we didn't cover that much in Sweden.

    We got this review for some California state test or something and this question is kind of weird. If I worked this problem correctly, steps B, C, and D all contain errors. However, the question says only one of them has an error. I provided a picture of the question at the bottom. Can someone tell me the answer as well as how they worked it? Maybe I just solved it wrong.

    http://img89.imageshack.us/img89/7448/20091859.png
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  2. #2
    Member SENTINEL4's Avatar
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    At step C it should be 6y>=38 not 6y<=38. When you multiply with a negative number the inequality symbol changes. (Hope you understand what i mean)
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  3. #3
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    Quote Originally Posted by SENTINEL4 View Post
    At step C it should be 6y>=38 not 6y<=38. When you multiply with a negative number the inequality symbol changes. (Hope you understand what i mean)
    I originally thought that too. However, look at B. It says 7-6y≥24 when it clearly should be 7-6y≥31. Wouldn't that make B the correct answer as well?

    I'm confused
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  4. #4
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    Quote Originally Posted by ComradeNF View Post
    Whats up people. I'm in Trig/PreCalc in school but I just moved to the United States a couple months ago so I never fully studied absolute value, since we didn't cover that much in Sweden.

    We got this review for some California state test or something and this question is kind of weird. If I worked this problem correctly, steps B, C, and D all contain errors. However, the question says only one of them has an error. I provided a picture of the question at the bottom. Can someone tell me the answer as well as how they worked it? Maybe I just solved it wrong.
    1. Use the definition of the absolute value: |7-6y|=\left\{\begin{array}{lcr}7-6y & if & 7-6y \geq 0 \implies y\leq \frac76 \\ -(7-6y) & if & 7-6y < 0 \implies y>\frac76 \end{array}\right.

    2. That means you'll get:

    7-6y\geq 31 \ and\ y \leq \frac76 ~~ \bold{or} ~~ -(7-6y) \geq 31 \ and\ y > \frac76

    3. Solve for y. Compare with the given answers. You'll notice that answer b) contains an error because in the 2nd inequality the summand 7 was subtracted at RHS but not at the LHS.
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  5. #5
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    Quote Originally Posted by earboth View Post
    1. Use the definition of the absolute value: |7-6y|=\left\{\begin{array}{lcr}7-6y & if & 7-6y \geq 0 \implies y\leq \frac76 \\ -(7-6y) & if & 7-6y < 0 \implies y>\frac76 \end{array}\right.

    2. That means you'll get:

    7-6y\geq 31 \ and\ y \leq \frac76 ~~ \bold{or} ~~ -(7-6y) \geq 31 \ and\ y > \frac76

    3. Solve for y. Compare with the given answers. You'll notice that answer b) contains an error because in the 2nd inequality the summand 7 was subtracted at RHS but not at the LHS.
    But don't c and d contain errors as well? I believe the sign in d should be flipped if I am not mistaken.

    Thanks for the help, and sorry I ask so many questions xD
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  6. #6
    Member SENTINEL4's Avatar
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    Quote Originally Posted by ComradeNF View Post
    I originally thought that too. However, look at B. It says 7-6y≥24 when it clearly should be 7-6y≥31. Wouldn't that make B the correct answer as well?

    I'm confused
    I saw that too but i took it as a typographic error because at step c, 7 just go away and doesn't get substracted from both parts of the inequality
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  7. #7
    Member SENTINEL4's Avatar
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    Quote Originally Posted by ComradeNF View Post
    But don't c and d contain errors as well? I believe the sign in d should be flipped if I am not mistaken.

    Thanks for the help, and sorry I ask so many questions xD
    At d the right is y>=38/6 but it should be flipped after step b
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  8. #8
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    Everyone keeps talking about an error "at" a certain step. I think this is confusing. The error occurs in "going" from one step to another. In this question there is an error in going from step a to step b, but I believe that this is just a typo and the 7 should not be written in step b. There is a genuine error in going from step b to step c.
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  9. #9
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    Quote Originally Posted by ComradeNF View Post
    I originally thought that too. However, look at B. It says 7-6y≥24 when it clearly should be 7-6y≥31. Wouldn't that make B the correct answer as well?

    I'm confused
    Think of "modulus" as being the distance of a point on the vertical number line from 0.

    Then |7-6y|\ge\ 31

    means the point on the y-axis is either at +31 or above, or at -31 or below.

    Then step "a" is fine.

    There is an error at step "b" as you correctly pointed out.
    Subtract 7 from both sides for the part on the left,
    but they've only taken 7 from one side for the part on the right.

    Further errors are at part "c".

    -38\ge\ -6y\Rightarrow\ 6y-38\ge\ 0\Rightarrow\ 6y\ge\ 38

    However, they have "cancelled" their original error from "b" with the part on the right!

    7-6y\ge\ 31\Rightarrow\ 7\ge\ 6y+31\Rightarrow\ 7-31\ge\ 6y
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