If the inequality is a “≤”or “≥”, then the graph will be a closed half‐plane. This checking method is often simply used as the method to decide which half‐plane to shade. You should shade the side that does not contain the point (0, 0). Since the point (0, 0) does not make this inequality a true statement, If the coordinates you selected do not make the inequality a true statement, then shade the half‐plane not containing those coordinates. If the coordinates you selected make the inequality a true statement when plugged in, then you should shade the half‐plane containing those coordinates. To check to see whether you've shaded the correct half‐plane, plug in a pair of coordinates-the pair of (0, 0) is often a good choice. Now shade the lower half‐plane as shown in Figure 2, since y < x – 3. An open half‐plane does not include the boundary line, so the boundary line is written as a dashed line on the graph.įirst graph the line y = x – 3 to find the boundary line (use a dashed line, since the inequality is “<”) as shown in Figure 1.įigure 1. If the inequality is a “>” or “<”, then the graph will be an open half‐plane. Before graphing a linear inequality, you must first find or use the equation of the line to make a boundary line. The graph of a linear inequality is always a half‐plane. This line is called the boundary line (or bounding line). Quiz: Linear Inequalities and Half-PlanesĮach line plotted on a coordinate graph divides the graph (or plane) into two half‐planes.Solving Equations Containing Absolute Value.Inequalities Graphing and Absolute Value.Quiz: Operations with Algebraic Fractions.Quiz: Solving Systems of Equations (Simultaneous Equations).Solving Systems of Equations (Simultaneous Equations).Quiz: Variables and Algebraic Expressions.Quiz: Simplifying Fractions and Complex Fractions.Simplifying Fractions and Complex Fractions.Quiz: Signed Numbers (Positive Numbers and Negative Numbers).Signed Numbers (Positive Numbers and Negative Numbers).Quiz: Multiplying and Dividing Using Zero.Quiz: Properties of Basic Mathematical Operations.Properties of Basic Mathematical Operations.In reducing the transportation cost, etc. In maximising the output under the given condition.Various examples where the concept of compound inequalities is used are, Q6: What are the Applications of Compound Inequality?
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