Solve the inequality and write your answer in interval notation

Question

x^2+3x-10/x^2+3x-4>0

Answer 1

Hi Annie!

 

We start with

 

x²+3x-10/x²+3x-4>0

 

Then we set the top to 0, and solve for x.

We can do this by noticie the top factors to (x+5)(x-2) which means x=-5,2.

 

Next, we do the same for the bottom. We get x=-4,1.

 

Pick numbers between -infinity, -5, -4, 1, 2, +infinity. For example, -10, -4.5, 0, 1.5, 10.

 

Plug each of these into the original inequality. 

 

Check to see which ones are true and which ones are false.

 

For example, when x=0 we get

 

-10/-4=2.5>0 which is true.

 

If it turns out to be true, we take interval where the x value came from.

 

For example, the inequality was true when x=0, so we take the interval the 0 came from i.e. (-4,0).

 

The union (U) of all these intervals will produce the correct solution.

 

I hope this is helpful.

 

Best regards!