anonymous
  • anonymous
-12r + 28 ≤ -4(2r - 13) A) {r | r > -6} B) {r | r ≥ -6} C) {r | r ≤ -6} D) {r | r < -6} I believe it is C, but can anyone double check? The direction of the sign always confuses me.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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DebbieG
  • DebbieG
I don't think it's C. Can you show your work and we'll see where the error is?
anonymous
  • anonymous
Yes, Hold on one sec.
anonymous
  • anonymous
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DebbieG
  • DebbieG
In the last step, you divided both sides of the inequality by -4. What do you have to do when you multiply or divide by a negative number?
DebbieG
  • DebbieG
(I can't help but notice that you didn't write the inequality symbol in that step anymore, lol)
anonymous
  • anonymous
:) Thats because the only thing I don't understand is when and when not switch the direction of the sign. I can get the answer, I just don't know when to switch the sign,
DebbieG
  • DebbieG
OK, let's get you over that little hump. :) Solving an inequality is JUST LIKE solving an equation. the only thing you need to remember is that, if you MULTIPLY or DIVIDE by a NEGATIVE NUMBER, then you must SWITCH THE DIRECTION of the sign. That's it! Switch, ONLY if, you mult or divide by a negative. NOT if you add or subtract stuff. NOT if you mult or divide by a POSITIVE number. WHY? think about it: -3<4 Now multiply both sides by -2: 6>-8 right??? But: if I have -3<4 and I multiply by +2, I just get -6<8. Still true. Try it with some different simple numbers, the ONLY time the sign needs to flip, is if you.... ....what?..... .... SAY IT WITH ME: MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER. :)
anonymous
  • anonymous
So then this one would be B, because I'm dividing 24 by a negative 4?
DebbieG
  • DebbieG
Sorry... stepped away from the computer. :) Yes, it would be B. Not so much "because you divided by a negative 4", but because that's how the solution works out. What I mean is, notice that if you ADDED the 12r to both sides and SUBTRACTED 52 to both sides, then you would have never had a negative coefficient on the r, and would have divided by +4 in the final step, so no flipping of the inequality. BUT, the r term would be on the other side of the inequality, so you would still end up with the same solution, r>=-6. E.g., just from a strategic point of view, sometimes the side you move the variable terms to can avoid that negative division. But it won't change the answer! If I have: 2x-3>-4x+1 and I subtract the 2x and subtract the 1: -4>-6x Now divide by negative so flip the sign: 4/62/3 Now instead if I have: 2x-3>-4x+1 and I add the 4x and add the 3: 6x>4 x>4/6 x>2/3 See, same thing, and I never had to flip!
anonymous
  • anonymous
Thanks Debbie! :)
DebbieG
  • DebbieG
You're welcome, happy to help. :)

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