We are given the inequality :
- 12 - 15 x > - 72
in order to solve for it, we need to isolate the term in x on one side, and finally isolate the variable x completely.
In order to have the term with "x" as a positive term, (that way making the final step of x solving easier), we add 15 x to both sides of the inequality:
- 12 - 15 x + 15 x > - 72 + 15 x
-12 > - 72 + 15 x
Now we add 72 to both sides in order to isolate the term in x on the right, and group all the pure numerical terms on the left:
- 12 + 72 > -72 + 72 + 15 x
60 > 15 x
now we proceed to diide by 15 (which is a positive numebr and therefore doesn't change the direction of our inequality:
60 / 15 > 15 x / 15
4 > x
So the answer is all the real numbers "x" strictly smaller than 4.
On the number line this x < 4 is represented by a highligted horizontal band to the left of the point "4" on the number line. Make sure that the point "4" is NOT counted. So you will have to have either a parenthesis drawn at the number 4, or an "empty dot" at the point 4 on the line.