RealityWillSlapYou
  • RealityWillSlapYou
Is this correct? 12 + 4x ≤ 5x -2 12 -x ≤ -2 -x ≤ -14
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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JamesJ
  • JamesJ
Yes, but we would never express the answer that way. You want an inequality involving only x, not -x, hence .... x ....
RealityWillSlapYou
  • RealityWillSlapYou
Oh, okay so it's x ≤ -14?
JamesJ
  • JamesJ
No. Careful. a < b <=> -a > -b

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RealityWillSlapYou
  • RealityWillSlapYou
?
JamesJ
  • JamesJ
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.
RealityWillSlapYou
  • RealityWillSlapYou
Okay, so is all of it wrong?
JamesJ
  • JamesJ
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 \[ x \geq 14 \]
RealityWillSlapYou
  • RealityWillSlapYou
Oh, okay I get it now. So I should shade it to the left, correct?
JamesJ
  • JamesJ
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.
RealityWillSlapYou
  • RealityWillSlapYou
Closed circle shade to the right?
JamesJ
  • JamesJ
Yes, as the shaded circle indicates you include that value, in this case 14.
JamesJ
  • JamesJ
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.
RealityWillSlapYou
  • RealityWillSlapYou
Okay, thank you so much! o( ̄∇ ̄o)

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