Question

Solve the inequality, (x+3)(x-2)>0. Express your answer using set notation.

Answer 1

Imagine x is a big negative number? What will the result of this expression be?

Answer 2

(x+3)(x-2) is 0 when x=-3 and 2. So use test points before and after -3 and 2 to see what are happening to the factors.
so plug in some number before -3 like -4
so -4+3=-1
-4-2=-6
(-1)(-6)=6>0 so part of the solution is x is (-inf,-3)
now plug in a number between -3 and 2 like 0
so 0+3=3
0-2=-2
(3)(-2)=-6<0 so the interval (-3,2) is not apart of the solution
now you do the last interval

Answer 3

If x is a big negative numer x+3 will still be big and negative, and x-2 will also be negative. A negative times a negative is positive. So big negative values for x are ok.

Answer 4

Now as x gets close to -3 from the negative infinity side, the (x+3) factor will start getting closer and closer to 0.

Once x = -3 we see that the expression becomes 0, so this is not allowed.

Answer 5

So our first interval is \((-\infty,-3)\).

Now if x is between -3 and 2 what will this expression be?

Answer 6

so the last interval would be, (2,inf)?

Answer 7

is that part of the solution?
let's check:
3+3=6
3-1=2
6(2)>0 so yes thats right so your whole answer is (-inf,3)U(2,inf)

Answer 8

that 3 is suppose to be negative

Answer 9

(-inf,-3)U(2,inf)

Answer 10

is that part of the solution?
let's check:
3+3=6
3-1=2***
6(2)>0 so yes thats right so your whole answer is (-inf,3)U(2,in

*** the 3-1, isnt it suppose to be 3-2?

Answer 11

yes but we still get something positive no biggie little type-0