x^2 +2x -3>0
I don't understand when to use the union symbol After using my three test points. i know the answer is (x-1)(x+3) so x = -3 X= 1
You are asking for a hard and fast rule which does not exist.
In general, quadric inequalities can have the whole line as a solution set, such as
Or the solution set can be between to real numbers, as in the set is .
Out side two numbers: , solution .
But that is only a rule of thumb.
Are you saying that you do not know what the union symbol means?
The fact that x= -3 and x= 1 make the two sides equal tells you that the inequality is one way or the other through out the three intervals, , , and . Plato told you that the solution cannot be (1, 3) because x= 0 is in that interval and 0 does not satisfy the inequality. You really should, then, check one point in each of the other intervals. x= 2 is in the interval . so x= 2 and, so, every number in satisfies it. x= -4 is in and so x= -4 and, therefore, every number in satisifes the inequality.
That is, any number in or in will satisfy the inequality. A point is in if and only if it is in A or in B, by definition.
You answered the question. Thank you, for understanding what I was trying to convey. I assumed I broke it clearly down to what I did and didn't understand, but I guess people are in a rush and only wish to explain the answer. Thank you so much for being patient and throughly explaining everything.