Question

I know this sounds kinda dumb, but while graphing an inequality how do you know which side to shade in? I have a note that says use (0,0) as a test point if does not satisfy do opposite of boundary line. I'm lost how would I test it

Answer 1

One trick is to always write the inequality with the variable on the left side. This is frequently taught in the lower grades.
When you do this, you will always shade in the direction indicated by the inequality sign.
1) With x<3, shade the left; notice the arrow points to the left
2) With x>4 shade the right; notice the arrow points to the right
3) With 5<x, flip it to x>5; notice the inequality still points to the 5; now shade the right
4) With 6>x, flip it to x<6; notice the inequality still points to the x; now shade to the left

Another way is to always test a point on one side of the number in the inequality
1) Given x<3, you may choose to try 5
Look at putting the 5 in place of the x; 5<3; this is a false statement so do not shade the side with the 5 (to the right of 3), shade the other side of 3 (to the left of 3)
2) Given x<3, you may choose to try 2
Look at putting the 2 in place of x; 2<3; this is a true statement so shade the side with the 2
This method help you more in understanding why you are shading the side the shade. You want to shade the side that has numbers which will make you statement a true statement.
Good Luck! Hope you understand a little better now!

Answer 2

Thank you

Answer 3

What if the inequality is y<-3/4x+3