Q: Solve: 0 < (3x+6)^-1< 1/3
A: First we must remember what it means to have “-1” as a power. The “negative” puts us down in the denominator and the “1” means there is only 1 of the term… Examples:
4^-1 = 1/4
4^-3 = 1/4³ = 1/64
Make sense?
On to the problem:
0 < (3x+6)^-1< 1/3
0 < 1/(3x + 6) < 1/3
Clear the denominator by multiplying everything by (3x + 6):
(3x + 6)*0 < (3x + 6)*1/(3x + 6) < (3x + 6)*(1/3)
Simplify
0 < (3x + 6)/(3x + 6) < (3x + 6)/3
0 < 1 < x + 2
We don’t need the part that tells us that 0 < 1… Useless info we already know :)… So:
1 < x + 2
Subtract 2 from both sides to get:
-2 < x
