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Math Help - What is the answer to: a+4 ≥ 2a?

  1. #1
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    What is the answer to: a+4 ≥ 2a?

    What is the answer to:

    a+4 ≥ 2a


    It asks you to isolate the variable.

    My answer booklet says the correct answer is
    4 ≥ a.

    I do not know how they reached this conclusion. My thought process told me to divide a+4 by a and then divide 2a by a. That left me with 4≥2.

    What am I doing wrong? How do i get the correct answer of
    4 ≥ a. My answer book does not explain it.

    Please Help!
    Your help is greatly appreciated!!
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: What is the answer to: a+4 ≥ 2a?

    Quote Originally Posted by gredude View Post
    What is the answer to:

    a+4 ≥ 2a


    It asks you to isolate the variable.

    My answer booklet says the correct answer is
    4 ≥ a.

    I do not know how they reached this conclusion. My thought process told me to divide a+4 by a and then divide 2a by a. That left me with 4≥2.

    What am I doing wrong? How do i get the correct answer of
    4 ≥ a. My answer book does not explain it.

    Please Help!
    Your help is greatly appreciated!!
    Your problem boils down to order of operations.
    \frac{a + 4}{a} \neq 4

    In fact
    \frac{a + 4}{a} = 1 + \frac{4}{a}

    We divide each term by a, not just the first one.

    The solution:
    a + 4 \geq 2a

    a + 4 - a \geq 2a - a

    Can you take it from here?

    -Dan
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  3. #3
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    Re: What is the answer to: a+4 ≥ 2a?

    Quote Originally Posted by topsquark View Post
    Your problem boils down to order of operations.
    \frac{a + 4}{a} \neq 4

    In fact
    \frac{a + 4}{a} = 1 + \frac{4}{a}

    We divide each term by a, not just the first one.

    The solution:
    a + 4 \geq 2a

    a + 4 - a \geq 2a - a

    Can you take it from here?

    -Dan
    Im sorry, but I still don't understand. Why are you subtracting a from 2a?

    Wouldnt that leave you with the number 2? I am not sure how you reached you answer. Could you give me a simpler explanation. I really appreciate it.
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  4. #4
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    Re: What is the answer to: a+4 ≥ 2a?

    I hope that the "gre" in "gredude" doesn't stand for "graduate record exam"! You are misundertanding things that are covered in a class for 12 to 13 year old students- and that follow directly from more basic arithmetic. No, "2a- a" is NOT 2. Subtracting a does not mean "erase the a". If you have two elephants and "take away" one elephant, you have left one elephant, not the number "2". If a= 5, 2a= 10 and 2a- a is 10- 5= 5= a.
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    Re: What is the answer to: a+4 ≥ 2a?

    I'm sorry, i don't understand. Please could you just go over the problem step by step. Im sorry, but I really need help!
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  6. #6
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    Re: What is the answer to: a+4 ≥ 2a?

    This is as far as I can understand.

    You are subtracting a from a+4. Which leaves you with 4. am I right so far??
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    Re: What is the answer to: a+4 ≥ 2a?

    Wait a second, is 4 ≥ a the same thing as saying 4 ≥ 1a. By subtracting afrom 2a, you are left with 1a or just a?

    So basically you subtracted a from both sides to get the answer... Is that correct?
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  8. #8
    Forum Admin topsquark's Avatar
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    Re: What is the answer to: a+4 ≥ 2a?

    Quote Originally Posted by gredude View Post
    Wait a second, is 4 ≥ a the same thing as saying 4 ≥ 1a. By subtracting afrom 2a, you are left with 1a or just a?

    So basically you subtracted a from both sides to get the answer... Is that correct?
    That is correct. Also, 1a = a.

    -Dan
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