Question

(x+4)(x-1)<0

Answer 1

(x+4)(x-1)<0, you can think of this inequality intuitively. For the product of (x+4) and (x-1) to be less than zero either (x+4) must be negative. i.e (x+4) < 0 or (x-1) must be negative i.e. (x-1) < 0. However, both cannot be negative since that would lead to the product of two positive numbers which will be greater than 0.

Solving these individual inequalities, we find that (x+4) < 0, x < -4 or (x-1) < 0, x < 1. Since only one expression, either (x +4) or (x-1) can be negative, we must have that
-4 < x < 1.

Answer 2

(x+4)(x-1)<0

If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0.
(x+4)=0_(x-1)=0

Set the first factor equal to 0 and solve.
(x+4)=0

Remove the parentheses around the expression x+4.
x+4=0

Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.
x=-4

Set the next factor equal to 0 and solve.
(x-1)=0

Remove the parentheses around the expression x-1.
x-1=0

Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.
x=1

To find the solution set that makes the expression less than 0, break the set into real number intervals based on the values found earlier.
x<-4_-4<x<1_1<x

Determine if the given interval makes each factor positive or negative. If the number of negative factors is odd, then the entire expression over this interval is negative. If the number of negative factors is even, then the entire expression over this interval is positive.
x<-4 makes the expression positive_-4<x<1 makes the expression negative_1<x makes the expression positive

Since this is a 'less than 0' inequality, all intervals that make the expression negative are part of the solution.
-4<x<1

Answer 3

^that too lol.