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