SOLUTION: Solve {{{7/(x^2-6x-16)<=0}}}

Question 135451: Solve
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's find the vertical asymptotes

Stet the denominator equal to zero

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So the vertical asymptotes are

or

This means that the critical values are and

So let's test a value that is to the left of

Start with the given inequality

Plug in

Simplify

Since is false, this means that the interval does not work

------------------------------------

So let's test a value that is in between and

Start with the given inequality

Plug in

Simplify

Since is true, this means that the part of the solution set is [

]

-------------------------------

Finally, let's test a point that is to the right of

Start with the given inequality

Plug in

Simplify

Since is false, this means that the interval does not work

----------------------------------------

Answer:

So the solution in interval notation is [

]
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