3n + 11 < 17 or -3n > 12. Which is the best description of the solution set?
n < 2 or n > -4
n < 2 or n < -4
n < 2
n < -4
3n + 11 < 17 or -3n > 12
-11 -11
------------------------
3n < 6 or -3n > 12
Write it without the space
3n < 6 or -3n > 12
Divide the left inequality through by 3
n < 2 or -3n > 12
Divide the right inequality through by -3, which reverses the inequality
n < 2 or n < -4
Place both inequalities on number lines
n < 2
<================================o--------
-6 -5 -4 -3 -2 -1 0 1 2 3 4
n < -4
<========o--------------------------------
-6 -5 -4 -3 -2 -1 0 1 2 3 4
Now since the word between the two inequalities is "OR"
our final answer only has to be such that it will be true
that if we pick any value in the shaded region of the
graph of our final answer, then at least one of them must
be true, and it is NOT NECESSARY that BOTH of them be true,
so we only need to use the first one,
<================================o--------
-6 -5 -4 -3 -2 -1 0 1 2 3 4
So the correct answer is the next to last one:
n < 2
[Note that if the word between them had been "AND" instead of
"OR" then the answer would have been n < -4, for we then would
have had to made sure that BOTH inequalities were true for any
value that was picked in the shaded region of the final answer,
but since it is "OR" we only have to make sure that one, not both,
of them is true.]
Edwin
