Question

true or false the origin would be included in the solution set for the following inequality y>3x-9

Answer 1

Well, if the origin is part of the solution set, then it will work in the inequality. You should try plugging in the value and see if its true or not.

Answer 2

ok

Answer 3

The origin is the point (x, y) = (0, 0).
Plugging it in for the x and y, we get:
0 > 3*0 - 9
Then we just simplify it down. If it is true, then (0, 0) is part of the solution set. Otherwise, it is not.

Answer 4

how do you know when the origin of an soultion set is included in an inequality

Answer 5

The origin is part of the solution set if it works in the inequality. Consider, for example, if we had the inequality:
x < y + 1
This is a pretty simple inequality, but if we plug in (0, 0), it works:
0 < 0 + 1 -> 0 < 1 true
So, the origin is part of the solution set for this inequality.

Answer 6

What the "solution set" essentially is, is just a collection of the points that make the inequality true. If a point is "in" the solution set, then it is one of the points that makes the inequality true. If it is not in the solution set, then the point makes the equation false.