Which points satisfy the inequality

These values are located in the shaded region, so are solutions. These values are not located in the shaded region, so are not solutions. Plotting inequalities is fairly straightforward if you follow a couple steps. You can use the x — and y -intercepts for this equation by substituting 0 in for x first and finding the value of y ; then substitute 0 in for y and find x. The next step is to find the region that contains the solutions. Is it above or below the boundary line?

To identify the region where the inequality holds true, you can test a couple of ordered pairs, one on each side of the boundary line. This is true! Plot the points, and graph the line. Find an ordered pair on either side of the boundary line. When inequalities are graphed on a coordinate plane, the solutions are located in a region of the coordinate plane, which is represented as a shaded area on the plane. You can tell which region to shade by testing some points in the inequality. Using a coordinate plane is especially helpful for visualizing the region of solutions for inequalities with two variables.

Skip to main content. Graphing inequalities review. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Voiceover] We have two inequalities here, the first one says that x plus two is less than or equal to two x. This one over here in I guess this light-purple-mauve color, is three x plus four is greater than five x. Over here we have four numbers and what I want to do in this video is test whether any of these four numbers satisfy either of these inequalities.

I encourage you to pause this video and try these numbers out, does zero satisfy this inequality? Does it satisfy this one? Does one satisfy this one?

Does it satisfy that one? I encourage you to try these four numbers out on these two inequalities. Assuming you have tried that, let's work through this together. Let's say, if we try out zero on this inequality right over here, let's substitute x with zero.

So, we'll have zero plus two needs to be less than or equal to two times zero. Is that true? Well, on the left hand side, this is two needs to be less than or equal to zero. Is that true, is two less than or equal to zero? No, two is larger than zero. So this is not going to be true, this does not satisfy the left hand side inequality, let's see if it satisfies this inequality over here.

In order to satisfy it, three times zero plus four needs to be greater than five times zero. Well three times zero is just zero, five times zero is zero. So four needs to be greater than zero, which is true.

So it does satisfy this inequality right over here so zero does satisfy this inequality. Let's try out one. To satisfy this one, one plus two needs to be less than or equal to two. The graph of this equation is a line. Finally, pick one point that is not on either line 0 , 0 is usually the easiest and decide whether these coordinates satisfy the inequality or not. If they do, shade the half-plane containing that point.

If they don't, shade the other half-plane. Graph each of the inequalities in the system in a similar way. The solution of the system of inequalities is the intersection region of all the solutions in the system.

This is false. So, the solution does not contain the point 0 , 0.