More Inequality Solving

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

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