Answer :
x²+5x-24<0
(x+8)(x-3)<0
treat the "<" sign as a "=" sign, you have x=-8, and x=3
take a number smaller than -8, say -9, plug x=-9 in to inequality to see if it works: (-9+8) is a negative, (-9-3) is a negative, the result is a positive, >0, so it doesn't work.
Next, take a number between -8 and 3 and a number larger than 3 to try, you'll see that the answer is -8<x<3
(x+8)(x-3)<0
treat the "<" sign as a "=" sign, you have x=-8, and x=3
take a number smaller than -8, say -9, plug x=-9 in to inequality to see if it works: (-9+8) is a negative, (-9-3) is a negative, the result is a positive, >0, so it doesn't work.
Next, take a number between -8 and 3 and a number larger than 3 to try, you'll see that the answer is -8<x<3