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The Method of Inequality

Inequalities look similar to equations when written out; the primary difference is the sign between the left and right sides of the expression. Instead of reading "x = 2" or "y = x^2 - 6," both of which are equations, inequalities might read "x > 2" (x is greater than 2) or "y < x^2 - 6" (y is less than x^2 minus 6). When you graph inequalities, your results will look somewhat different than when you graph equations.
  1. Y Greater than X

    • For the inequality y > x, you would draw circles at two or three of these ordered pairs on a graph paper: (0, 0), (1, 1), (2, 2) and so on. This represents the line going through the origin with a slope of 1. Then you would draw a dotted line through those points and draw arrows on both ends signifying that the dotted line goes on infinitely. Next, you would shade in the area of the graph above the line. This shaded area indicates your solutions. The reason you dot the line and circle the points is that those indicate the boundary of the solutions -- but are not included in the solutions.

    Y Greater than or Equal to X

    • For this inequality, you would write "y > x" and then draw a line under the ">" sign. Then, instead of just drawing circles, you would fill them in and make a solid line. Then, shade the area above as you did for Section 1. All of the shaded area indicates possible solutions, but so do the points on the line.

    Y is Less than X

    • For "y < x," you would draw circles at the same points as in Section 1, and you would draw the same dotted line. You would then shade in the area beneath the line. All of your solutions would be in the shaded area -- and not on the line.

    Y is Less than or Equal to X

    • As in Section 2, you would draw a line under the "<" sign in "y < x." Then, you would color in the points and draw a solid line through them, and shade in the area beneath the line on the graph. The line and the shaded areas represent the possible solutions to the inequality.

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