Chatting about inequality exercise

[Mathesy]

if -1 ≤ x ≤ 2 and 1 ≤ y ≤ 3 then least positive value of (2y -3x) is

suppose
x = 2 as x ≤ 2 and
y = 3 as y ≤ 3
so
(2 x - 3 y) = (2*2 – 3*3)
= (4-9)
= (-5)
So ans is (2 x - 3 y) < -4

But the answer given is (2 x – 3 y) ≥ -4 HOW

Hi,

This is very simple. You have correctly arrived to the point where (2x-3y)<-4, and -5<-4, so, to get your positive values, you are supposed to multiply the whole inequality by a -1, which makes the relationship indicator CHANGE into a more than or equal. Therefore, your final answer is (2 x – 3 y) ≥ 4. So, 4 is your final answer.

Hope this helps.

 

[Deleted member 4993]

Hi,

This is very simple. You have correctly arrived to the point where (2x-3y)<-4, and -5<-4, so, to get your positive values, you are supposed to multiply the whole inequality by a -1, which makes the sign CHANGE into a more than or equal. Therefore, your final answer is (2 x – 3 y) ≥ 4. So, 4 is your final answer.

Hope this helps.

The OP is asked to find the LEAST positive value of (2y-3x) given -1 ≤ x ≤ 2 and 1 ≤ y ≤ 3 ................ edited

(2x-3y)≥ 4 cannot be the answer because @ x=2 and y = 1 we get (2x-3y) = 1 < 4

or

(2y-3x) ≥ 4 cannot be the answer because @ x=1 and y = 3 we get (2y-3x) = 3 < 4................ edited

To paraphrase pka - there are problems with the problem statement.

 

[pka]

The OP is asked to find the LEAST positive value of (2x-3y) given -1 ≤ x ≤ 2 and 1 ≤ y ≤ 3
To paraphrase pka - there are problems with the problem statement.

Moreover the OP is

if -1 ≤ x ≤ 2 and 1 ≤ y ≤ 3 then least positive value of (2y -3x) is

Why and/or how did (2y-3x ) get mysteriously changed to (2x-3y)?

Also in this reply,

to get your positive values, you are supposed to multiply the whole inequality by a -1, which makes the sign CHANGE into a more than or equal.

The statement in red is mathematically incorrect.

 

[Mathesy]

The statement in red is mathematically incorrect.

The statement in red is mathematically correct. Once you have an inequality that looks like this: -x>b, where b is a real number, it is recommended that you get rid of the negativity of the X. So, you multiply the whole inequation by a -1, and your relationship indicator changes to make it true. So, your result will then be x<-b.

So, in this case (although I have doubts whether the whole thing is there and nothing is missing), (2x-3y)<-4, when numbers used are the 2 for x and 3 for y, the final result is -5<-4. If he is asked to have the least positive value, multiplying the -5<-4 by a -1, gives us inequation that looks like this: 5>4, which explains the book's relationship indicator change. However, if we looked at our starting point and all the conditions given, it is impossible to have a 4 as the least positive value. Therefore, the answer given is mathematically incorrect. My attempt to prove it was not. However, the proof was poor. Dismissing that, and going from the starting point:

So, again, looking at the starting point (2y-3x), and x can be -1, 0, 1, 2, and y can be 1, 2, 3, then we are able to say that x=-1, and y=3, which leads us to a result of a positive value of 9. (2 times 3 - 3 times -1)=(6+3)=9

But, if we are supposed to suppose that x=2 and y=3, your answer is 0. Why, because you are messing your x, y order. It is 2y-3x, not 2x-3y. Or is it? BE CLEAR. So, 2times3 - 3times2 = 6-6, which is a 0. So, this complete posting makes no sense to me whatsoever. And, now I see that pka stated the same thing. So, I guess we need to know where the x stands and where the y stands first, and see if we can assume any numbers from the grouping given or not.

 

[JeffM]

Oh my goodness. Just acknowledge that you meant the relationship indicator and not the sign. And edit your post to correct the error. Every tutor makes mistakes, and every tutor should want to have them pointed out promptly to prevent confusing the student.