Question

What is the solution to the inequality -50 n < 10 ?

Answer 1

When we solve inequalities, wich are different from the "equalities" or you know them better as "equations".
We are not looking for one answer, but for all of the values the variable can take that satisfies the inequality.
in order words, the problem asks for the values of "n" that makes the equation "-50n" less than ten.

So we begin by asking ourselves "okay, but. What values would make 'n' equal 10?"
Si instead of writing a "<" we write a "=".
\[-50n=10\]
So let's solve for "n" and see what we get:
\[n=\frac{ 10 }{ (-50) }\]
\[n=-\frac{ 1 }{ 5 }\]
So now we have found the value that makes the equation "-50n" equal to 10, now we have to study it's sign:

now, all the values to the right of "-1/5" have a "-" wiritten because they are all les than 10, and for the other side, the left side, al have a "+" sign written because they are all greater than 10.
So, we will only accept all the values, not including "-1/5" that have the "-" sign wich would mean all the values lesser than 10, we write it like this:
\[S:(-\frac{ 1 }{ 5 },+\infty )\]
it reads "The solution are all the values of 'n' from -1/5 to positive inifinity, not including the value n=-1/5"