Solve each rational inequality. Give the solution set in interval...

Question

Solve each rational inequality. Give the solution set in interval notation.
(9x-8)/(4x^2+25)<0

Accepted Answer

Solve the following inequality and express the answer and interval notation where we have X minus 1/5 X squared plus 64. Less than zero. We want to do first to determine our intervals do that. We'll set our numerator equal to zero. Then the denominator equal to zero. Let's say we have 11 X minus one is equal to zero and five X squared plus 64 is equal to zero. Let's go ahead and solve for X here. Add one to both sides. We get 11 x is equal to one by, by 11 X is 1/11. Let's check our other answer. We have five X squared plus 64 track 64. We get five X squared is equal to negative 64/ X squared is negative 64/5 X would then be the square root of negative 64/5. Now we notice here we have a negative on the square root. That means do not have a real answer here. This is a complex answer. So we will now disregard are X equals square of negatives. For over five was like at the X equals 1/11. So then we can make another line 1/11. Now we have two intervals, everything below 1/11, everything above 1/11. We want to check which side is less than zero. So let's choose an arbitrary value. Let's say X is equal to zero here and X is equal to one here. We'll take this and plug into our equation zero. Give us 11 times zero minus 1/5 times zero squared plus 64. Simplified. This is negative 1/64. You will say this side is negative For you to play game. one is this equation. We would get 10 Over 69, which is positive. We want everything that's less than zero. So we just want the negative intervals. That means the answer to our problem then turns out to be negative infinity until we get to 1/11. We can then notice the answer to our problem is answer a okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Solve each rational inequality. Give the solution set in interval notation. (9x-8)/(4x^2+25)<0