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One point in each interval. An entire interval, between two critical points, either fulfills, or doesn't fulfill, the inequality.

For example, (x-3)(x+5) > 0; the corresponding equality is (x-3)(x+5) = 0, with the two critical points x = 3 and x = -5. The intervals that must be checked are x < -5, x between -5 and 3, and x > 3.

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Q: Why is it usually only necessary to test one point when graphing an inequality?

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One variable inequality- graph the point on the number line then choose a point on the point, to the left and to the right to see what gets shaded. Two variable inequality- graph the line on grid paper then choose a point on the line, to the left and to the right to see what gets shaded.

Linear programming is just graphing a bunch of linear inequalities. Remember that when you graph inequalities, you need to shade the "good" region - pick a point that is not on the line, put it in the inequality, and the it the point makes the inequality true (like 0

Take a sample point from either the top or bottom of the graph. I like to use (0,0) if it is not on the line. Substitute it into the inequality and if it is true then it represents all points on that line as true and vice versa.

Choose any point and substitute its coordinate into the inequality. If the inequality remains TRUE then the region containing the inequality is the one that you want. If it is false, then you want the region on the other side of the line. You can choose any point in the plane and substitute its coordinates into the inequality. The origin is usually the simplest.

Graphing or plotting.

An open or closed circle are used to graph an inequality in one variable. An open circle is used if the value at the end point is excluded from the feasible region while a closed circle is used if the value at that point is within the accepted region.

When the line goes through the origin like y>3x. Notice that there is no constant added to the end.

I think that you are asking about the linear inequalities with two variables, so my answer is related to them. First, you have to draw the boundary line (be careful, if your inequality does not contain the equal sign, the boundary line will be a dashed line, because the points on the line are not solutions to the inequality), which divide the coordinate system in two half-planes. Second, you have to test a point on either sides of the line (the best point is the origin, (0, 0), if it is not on the boundary line). If that point satisfies the inequality, then there are all its solutions, otherwise they are to the opposite side.

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Pick a test point, (the origin is the most convenient unless the line of the inequality falls on it), and plug it into the same linear inequality. If the test point makes the inequality true, then shade that side of the line. If the test point makes the inequality false, then shade the opposite side of the line.

the easiest way to do this is get a picture of a turtle. Place it over a sheet of graphing paper. place a point at every point that you can. Move the picture- you don't need it anymore. Connect the dots.

An equality defines a specific point (or points). An inequality can define an interval.

substitute the numbers into the inequality and see if it is true. EX: x > y+ 3 for the point (1, 6) .... 1 > 6 + 3 is not true so this point is not a solution.

It is because all measurements are taken from that point: it is the fixed point of reference.

When you graph a line using only the slope and a point, you start by graphing the point.

Draw the graph of the corresponding equality. This will divide the Cartesian plane into two parts.Evaluate the inequality for the origin, O - the point (0,0). Any point will do, but O it is easy to evaluate it there.It the inequality is true, then the part of the plane that contains the origin is the valid region whereas if the inequality is false, the other region is valid.

The solution is the coordinates of the point where the graphs of the equations intersect.

It can be a ray if it does not include the end point or a half line if it includes the end point.

It depends upon the inequality. All points on the line are those which are equal, thus:If the inequality is (strictly) "less than" () then the points on the line are not included; howeverif the inequality is "less than or equals" (â‰¤) or "greater than or equals" (â‰¥) then the points on the line are included.

The points of intersection are normally the solutions of the equations for x and y

You draw a number line. Then put a dot at the point at x. Happy graphing!

you cannot determine the exact value of the point

Graph as though the inequality is an equality. Then, find a point on one side of the line and see if it makes the inequality true. If it is true then that side gets shaded.

Arrange the inequality so that the variable is on the left. ex x < 7 If not equal to put an open circle at the number (7 in my example) if less than shade the number line to the left ( less than = shade left) if greater than shade right. If equal to put a point ( shaded dot) on the number follow same rules for shading