It's valid but you will then need to consider two cases. When n > 7, the denominator is negative and so will change the sign of the inequality.
So Case 1: n < 7
So the values of n which satisfy this case are
Now consider Case 2, where n > 7...
Just looking for some guidance on the following problem:
Find the least value of n (Natural number) for which (5n + 3 / 7 - n) < 1, n <> 7
One approach:
5n + 3 < 7 - n
6n + 3 < 7
6n < 4
3n < 2
n < 2/3
Since n is a Natural number we get n = 0 as the least value
The 1st step above involves multiplying across by 7 - n, however 7 - n is negative for n > 7 so this would equate to multiplying an inequality by a negative number in which case the sign would have to be changed.
Is it valid to multiply across by 7 - n as described?
Thanks
Corbomite1
It's valid but you will then need to consider two cases. When n > 7, the denominator is negative and so will change the sign of the inequality.
So Case 1: n < 7
So the values of n which satisfy this case are
Now consider Case 2, where n > 7...
Thanks for the quick reply! I have 2 further questions:
In case 1 above we have n < 7 which means 7 - n > 0 so we should be able to multiply across by 7 - n without changing the sign, yet you have changed the sign when arriving at 6n + 3 > 7
In case 2, n > 7 which means 7 - n < 0 so we need to change the sign when multiplying across by 7 - n:
5n + 3 / 7 - n < 1
5n + 3 > 7 - n [change sign]
6n + 3 > 7
6n > 4
3n > 2
n > 2/3
So this case cannot yield the least value of n for which the inequality holds, so we revert to n < 2/3 which gives n = 0 as n has to be a Natural number.
Correct?
Thanks a lot
Corbomite1