Question

Check my work? I feel I did something wrong.

–2x + 1 ≤ –11

My answer:

My final answer is x greater than or equal to 6 I got this from subtracting 1 to both sides. After you do that you should get -2x less than or equal to -12. Then you will need to divide -2 to both sides and you will get x is less than or equal to 6. You will need to flip the inequality. So your final answer will be x is greater than or equal to 6

Answer 1

I'm not sure if you are suppose to flip or not. I thought you were but on some other problems i'm not flipping and getting it right. Did I just submit a whole project completly wrong because I flipped the signs...

Answer 2

your correct\[x \ge6\]

Answer 3

Alright so I am suppose to flip my signs if I divide?

Answer 4

Its because it has the = part.

Answer 5

so if it was just < than u wouldnt flip it.

Answer 6

OHH Wow thank you so much. No wounder I have been getting some things wrong. Thanks so much @Rosa34! :D

Answer 7

u welcome!

Answer 8

The inequality sign flips if you multiply or divide both sides by a negative number.
Since in your case, solving the inequality involved dividing both sides by -2, (a negative number) the inequality sign flipped.
It has nothing to do with \(<\) vs \(\le\) or \(>\) vs \(\ge\)..
It only depends on multiplying or dividing both sides by a negative number.

Answer 9

@Rosa34 Read my comment above.

Answer 10

solve the same problem, \[-2x+1<-11\] with this sigh you do the same steps but the sigh does change please explain that.

Answer 11

for mathstudent55

Answer 12

@Rosa34 use the @ to tag people :P And anyway @mathstudent55 and @Rosa34 quick question.Why do I need to flip the inequality symbol when you divide by a negative number? I understand you need to do that but why?

Answer 13

@Gerald_69 I'll answer you very soon.

Sure, @Rosa34

\(-2x+1<-11\)

Subtract 1 from both sides:

\(-2x<-12\)

Divide both sides by -2, remembering to flip the inequality sign.

\(x > 6 \)

That's the final answer.

Answer 14

@Gerald_R9

Just notice the following:

-5 < 5 is a true statement. You agree right?

Answer 15

agree

Answer 16

Now if you multiply both sides of that true statement by -1, what do you get?

-5(-1) < 5(-1)

5 < -5 which is not a true statement.

On the other hand, if you flip the sign, it will be again a true statement.

5 > -5

Answer 17

ok your write i'll find better way of explaining myself @mathstudent55 especially to other people.

Answer 18

right

Answer 19

Oh alright so if you don't flip it, then the statement will not be true. Like -x+3>7 after doing all the work you will have x>-4 but it's not true till you flip it which the final anser will be x<-4

Answer 20

@Rosa34 The problem with your explanation above is not that you did not explain yourself clearly. You were very clear in your explanation. It's simply that your explanation is incorrect. The flipping of an inequality sign in an equation has nothing to do with a difference of whether the inequality sign has or does not have an equal sign with it. The flipping only depends on whether you are multiplying or dividing both sides of the inequality by a negative number.

Answer 21

got it @mathstudent55

Answer 22

@Gerald_R9 Yes you are correct. In the first step where you indicate division or multiplication by a negative number, you must flip the sign. I'll do your example and show you what I mean.

Answer 23

\(-x+3>7\)

Subtract 3 from both sides:

\(-x > 4\)

Divide both sides by -1:

\(\dfrac{-x}{-1} < \dfrac{4}{-1} \)
(Notice that since in this step I am already showing a division by a negative number, the sign has already flipped.)

Now we reduce both fractions.

x < -4

Final answer.

Answer 24

@Rosa34 Great.

Answer 25

Who knew a question would have sparked a learning session xD

Answer 26

This is the whole idea behind OS, isn't it?

Answer 27

Yes indeed :) You guys helped me expand my knowledge (nerd talk) :D

Answer 28

LOL. Good job, @Gerald_R9 , and thanks @Rosa34 for hanging in there and responding.

Answer 29

hey @mathstudent55 i got homework too and i know @Gerald_R9 has you to help him.