The first step we can take to find the simplest form of this inequality is to subtract 3 from both sides
[tex] \frac{1}{2} [/tex]n + 3 < 5
[tex] \frac{1}{2} [/tex]n + 3 - 3 < 5 - 3
[tex] \frac{1}{2} [/tex]n < 2
So now we have a simpler version to work with.
To further simplify, we can divide both sides by [tex] \frac{1}{2} [/tex]. Dividing by fractions is hard though, so smart people have found out that dividing by a fraction is the same as multiplying by that same fraction's reciprocal.
[tex] \frac{1}{2} [/tex]n / [tex] \frac{1}{2} [/tex] < 2 / [tex] \frac{1}{2} [/tex]
[tex] \frac{1}{2} [/tex]n * 2 < 2 * 2
Now, we can work it out to find the completely simplified inequality, which would simply be
n < 4
The character '<' represents that the number being represented by the variable is less than the number that follows that character. On a proper number line, this is represented by an open circle above the number on the right of the inequality with an arrow pointing the same direction on the number line that the point of the inequality symbol is facing.
If that doesn't make sense, imagine the inequality symbol as the head of an arrow.
<====<<
So the arrow would be pointing to the left, with an open circle above the 4. The only choice listed that represents this is the second option down.
Option B is your correct answer choice.
Hope that helped! =)
