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RealityWillSlapYou

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

  • one year ago
  • one year ago

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  1. JamesJ
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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 ....

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

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

    • one year ago
  4. RealityWillSlapYou
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    ?

    • one year ago
  5. JamesJ
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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.

    • one year ago
  6. RealityWillSlapYou
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    Okay, so is all of it wrong?

    • one year ago
  7. JamesJ
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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 \[ x \geq 14 \]

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

    • one year ago
  9. JamesJ
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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.

    • one year ago
  10. RealityWillSlapYou
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    Closed circle shade to the right?

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

    • one year ago
  12. JamesJ
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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.

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

    • one year ago
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