Six times a number decreased by 8 is less than five times the number plus 21

6 ( or any number that isn't a common multiple of 5 and 6 ) you should probably double-check just in case.

Step-by-step explanation:

Question = 6x - 8 < 5x +21

so we know that the product of 6x must be divisible by 6 and 5x must be devisable by 5.  so the first factor of 6 is 6 so:

(6 x 6) - 8 < (5 x 6) + 21

36 - 8 < 30 + 21

28 < 51

so x = 6

Honestly, any number would work because 6x is obviously more than 5x, but since for 6x you subtracting 8 and for 5x you adding 21 the answer will always be 6x - 8 < 5x + 21. Unless you use a common multiple of 6 and 5 as your x because then six times that number will always be more than 5 times that number. So for example 30 is a common multiple of 6 and 5 so:

(6 x 30) - 8 is more than (5 x 30) + 21

180 - 8 is more than 150 + 21

172 is more than 171

hope that helps  : )