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Math Help - solve using addition and multiplication principles

  1. #1
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    solve using addition and multiplication principles

    Did I do this correct? Its been about 10 years since i been to school and am having some issues remembering how to do a lot of this stuff.

    -6r-6 is less than or = to -2(2r-4)

    my work below:

    step 1: -6r-6 < or = to -4r+8

    step 2: -6+4r < or = to 8+6

    step 3: -2r < or = to 14/2

    step 4: -2r div -2r < or = to 7

    Answer: r > or = -7


    Let me know if i did this correct sorry i dont know how to type the correct characters for less than or = to or divide etc.

    Thanks in advance


    Mr.H
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  2. #2
    o_O
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    my work below:

    step 1: -6r-6 < or = to -4r+8

    step 2: -6+4r < or = to 8+6

    step 3: -2r < or = to 14/2

    step 4: -2r div -2r < or = to 7

    Answer: r > or = -7

    Your work is fine with a few minor technicalities. From going to step 2 to step 3, your inequality would not be true as it seems like you 'randomly' divided by 2 but I presume you're just getting ahead of yourself and was meant for step 3 to step 4.

    Also, I think you meant to divide both sides by -2 not -2r as you would end up with: \frac{-2r}{{\color{blue}-2r}} \leq \frac{14}{{\color{blue}-2r}} \: \: \Rightarrow \: \: -2 \geq -\frac{7}{r} which isn't necessary.

    In summary:
    \text{Step 3: } -2r \leq 14 (Didn't divide by 2 yet. Remember: What you do to one side you do to the other)
    \text{Step 4: }\frac{-2r}{{\color{blue}-2}} \leq \frac{14}{{\color{blue}-2}}
    \text{Answer: } r \geq -7
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  3. #3
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    Quote Originally Posted by o_O View Post
    my work below:

    step 1: -6r-6 < or = to -4r+8

    step 2: -6+4r < or = to 8+6

    step 3: -2r < or = to 14/2

    step 4: -2r div -2r < or = to 7

    Answer: r > or = -7

    Your work is fine with a few minor technicalities. From going to step 2 to step 3, your inequality would not be true as it seems like you 'randomly' divided by 2 but I presume you're just getting ahead of yourself and was meant for step 3 to step 4.

    Also, I think you meant to divide both sides by -2 not -2r as you would end up with: \frac{-2r}{{\color{blue}-2r}} \leq \frac{14}{{\color{blue}-2r}} \: \: \Rightarrow \: \: -2 \geq -\frac{7}{r} which isn't necessary.

    In summary:
    \text{Step 3: } -2r \leq 14 (Didn't divide by 2 yet. Remember: What you do to one side you do to the other)
    \text{Step 4: }\frac{-2r}{{\color{blue}-2}} \leq \frac{14}{{\color{blue}-2}}
    \text{Answer: } r \geq -7

    Yes,

    I also divded in my head the 14/2 by -2 i should have shown that work as part of step 4 but i am on the right track here which is good thank you for your response.


    Mr.Huge
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