six decreased by 3 times a number is less them 12. find the set of all such numbers.?

Answer 1

6-3x<12
-3x<12-6
-x< 6/3
x> -2

so xE ]-2; infinity[

Answer 2

6 decreased by 3 times a number is less than 12:

Let the unknown number be x.
6 - 3x <12

-3x < 6 (subtract 6 from both sides)
-x < 2 (divide both sides by 3)

x > -2 (divide by -1; note the inversion of the inequality sign)

Once x is an integer, it can be any number -1 or greater

i.e. {-1,0,1,2,3,...}

NB you can try a sample number within the range to verify
eg. let x = 10

6 - 3(10) = -24 ( which is less than 12)

Answer 3

Let

x = the number

6 - 3x < 12

The solution set to make this true

{ -1, 0, 1, 2, 3, 4, 5. . . . . }

- - - - - - - - - - - s

Answer 4

n = number

6 - 3n < 12

{-1,0,1,2,3...}