in this example. We're being asked to first all the giving compound inequality. Then we're going to draft the solution set on the number line. So remember to solve the given compound inequality, you're just gonna solve both inequality inequality separately. So let's start with our first one. X plus five is greater than eight. Well, to solve for X were simply just going to subtract five from both sides of firing equality. Well, eight minus five is three. So we're left with X is greater than three. Now, we'll solve our second inequality. We have negative. Three X is greater than 12. So the solve for X we're going to divide both sides of our inequality by negative three. Now, don't forget, when you divide both sides of an inequality by a negative value, we have to flip our inequality sign so it's not gonna be greater than it's now going to be less than. And then we have 12 divided by negative three, which is negative for So now we've solved both for inequalities. I'm just bringing down our work. Okay. The next thing we need to do is graft the solution set on the number line so we're going to set up a number line. Then we're gonna put our two critical values three and negative four. And remember, because negative four is less than three that needs to come on the left. Now remember to scrap compound inequalities that include that involve the words or the easiest way to do it is just graft Botham separately, just on the same number line. So let's start with X is greater than three. Well, because three is not included in solution, we're gonna have open circle at three. And because we're talking about values of X that are greater than three, we're going to shade to the right of that circle. So all of these values in this red shaded area will represent values of X that make the first inequality true. Now we can graph our second inequality. X is less than negative four. Well, that means that negative four is not including our solution set. So we have an open circle and where are values of X that are less than negative, for that would be to the left. So we're going to shade the left hand side. So now we've shaded are inequality, so you'll find a lot of the times when you're shaving or statements, you're gonna shade the outside. In the next couple examples, I'll show you some special cases, which is why, if you if you always go back to when you graph these on a number line, if you just grab both of them separately, you're gonna end up having the correct number line in the end.