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RealityWillSlapYou

  • 3 years ago

Is this correct? 12 + 4x ≤ 5x -2 12 -x ≤ -2 -x ≤ -14

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  1. JamesJ
    • 3 years ago
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    Yes, but we would never express the answer that way. You want an inequality involving only x, not -x, hence .... x ....

  2. RealityWillSlapYou
    • 3 years ago
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    Oh, okay so it's x ≤ -14?

  3. JamesJ
    • 3 years ago
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    No. Careful. a < b <=> -a > -b

  4. RealityWillSlapYou
    • 3 years ago
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    ?

  5. JamesJ
    • 3 years ago
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    if \[ -x \leq -14 \] that can NOT mean that \( x \leq -14 \). For example, when x = 15, \( -x = 15 \leq -14 \) is true, but \( x =15 \leq -14 \) is definitely false.

  6. RealityWillSlapYou
    • 3 years ago
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    Okay, so is all of it wrong?

  7. JamesJ
    • 3 years ago
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    No. What I am saying is you want to have an inequality involving only x, not -x. The inequality \[ -x \leq -14 \] is equivalent to \[ x \geq 14 \]

  8. RealityWillSlapYou
    • 3 years ago
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    Oh, okay I get it now. So I should shade it to the left, correct?

  9. JamesJ
    • 3 years ago
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    No. x is greater or equal to 14, so it is that part of the number line to the right of 14, including 14 itself.

  10. RealityWillSlapYou
    • 3 years ago
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    Closed circle shade to the right?

  11. JamesJ
    • 3 years ago
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    Yes, as the shaded circle indicates you include that value, in this case 14.

  12. JamesJ
    • 3 years ago
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    btw, whenever you do these things you should double check with the original expression. Put in x = 14 and x = 15 and make sure you get the results you expect.

  13. RealityWillSlapYou
    • 3 years ago
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    Okay, thank you so much! o( ̄∇ ̄o)

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