Question

Solve the inequality:
(5x + 4)(x - 4) < 0

Answer 1

Here is how I do these type of questions:

Critical values are x = -4/5 and x = 4

Mark these on a number line, splitting the number line into 3 distinct parts
< -4/5
between -4/5 and 4
> 4

Pick any value in each of the regions, if that value satisfies the original inequation, so will every other value in that region
You don't have to actually evaluate, just consider the sign
1. let x = -10
(-)(-) --> + , no good
2. let x = 0
(+)(-) --> , that works
3. let x = 10
(+)(+) --> + , no good

so -4/3 < x < 4