We are given the following equation and want to find the possible values of x
Subtract both sides by 3x
Now, we have this weird equation. Since -15 is NOT equal 15 and there is no other way we could have solved for x, there is no real solution to the given equation.
In other words, there is no value of x that makes the equation true.
Let me know if you need any clarifications, thanks!
~ Padoru
Part A:
You may choose the two lines connecting the origin and points A and B, and choose the portion of the space between them.
The line between the origin and A is
We want everything below this line (line included), so the first inequality is
The line between the origin and B is
We want everything above this line (line included), so the second inequality is
Create a system with these two inequalities and you'll have an area including only points A and B
Part B:
To verify the solutions, we can plug the coordinates of A and B in this system and check that we get something true: the coordinates of point A are (1,3), while the coordinates of point B are (3,1). The system becomes:
Which means
And these are all true. So, the system is satisfied, which means that the points belong to the shaded area.
Part C
If you draw the line, you'll see that the only points that lay below the line are B and C. In fact, if we plug the coordinates we have
And this are both true. You can check the coordinates of all other points, and see that they won't satisfy the inequality y<3x-6