Question

solve for x. Enter your answer in interval notation using grouping symbols.
x^2+5x<24

Answer 1

This is a quadratic inequality because of the x^2 so pretend it an equation, set it equal to 0 and solve be either factoring or quad formula

x^2 +5x - 24 = 0
(x+8)(x-3) = 0

so it is = 0 at x = -8 and x = 3

When is the inequality less than 0 (or negative)

We can test numbers like -10000 because that is to the left of -8

(-10000 + 8)(-1000 - 3) = a + number so it is above the x axis

a number between -8 and 3 is 0, so

(0+8)(0 - 3) is a neg number so the graph is below the x axis.

and a number bigger ( to the right ) than 3 is like 10000

(1000+8(1000-3) is + so above the x axis so the solution to the inequality is

(-8, 3)

in interval notation. Is that the "grouping symbols" you need?