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Table of Contents Solving Linear Inequalities Graphically It is assumed you already know how to solve linear inequalities algebraically. A inequality is a sentence using the symbols: The method of solving linear inequalities graphically will be discussed here. While there are several methods available, only one method will be shown. In this authors opinion it is the best and easiest.

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Table of Contents Example 1 Solve: Move all terms to the left hand side of the inequality. It doesn’t make any difference if we combine terms. Let y1 equal the left side.

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Table of Contents Since y1 is the left hand side, and 0 is the right hand side, we have … We want to find all x-values for which y1 is less than or equal to zero.

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Table of Contents Break this expression up into two parts, and consider what it means graphically. The y-values are negative means points are below the x-axis The y-values are zero means points are on the x-axis

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Table of Contents Enter the expression into y1 on the calculator. Graph using Zoom|ZStandard. Using Trace we find that the x-intercept is located at x = 5.

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Table of Contents Identify the portion of the graph where points are below the x-axis. The x-values corresponding to the points in red on the graph are the solutions to the inequality. Recall that we want to find all x-values for which y1 is less than or equal to zero.

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Table of Contents Write the answer based on the portion that is shaded green. Note that the inequality symbol is ≤, since the original problem included the equals symbol. Shade the portion of the x-axis that corresponds to the points in red.

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Table of Contents Example 2 Solve: Move all terms to the left hand side of the inequality. It doesn’t make any difference if we combine terms. Let y1 equal the left side.

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Table of Contents Since y1 is the left hand side, and 0 is the right hand side, we have … We want to find all x-values for which y1 is greater than zero.

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Table of Contents Consider what this means graphically. Since the y-values are positive, points are above the x-axis

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Table of Contents Enter the expression into y1 on the calculator. Graph using Zoom|ZStandard. To get a better view, use Window to set the x-values at [-5,20]

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Table of Contents Graph Using Trace we find that the x-intercept is located at x = 8.

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Table of Contents Identify the portion of the graph where points are above the x-axis. The x-values corresponding to the points in red on the graph are the solutions to the inequality. Recall that we want to find all x-values for which y1 is greater than zero.

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Table of Contents Write the answer based on the portion that is shaded green. Note that the inequality symbol is >, since the original problem did not include the equals symbol. Shade the portion of the x-axis that corresponds to the points in red.

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Table of Contents Original Inequality Important: compare the inequality signs … Answer In this problem, both signs are the same. This is not always the case! Use the green shaded line on the x-axis of your graph to determine the direction of the sign in the answer.

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Table of Contents

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EXAMPLE 6 Use a quadratic inequality as a model The number T of teams that have participated in a robot- building competition for high school students.

EXAMPLE 6 Use a quadratic inequality as a model The number T of teams that have participated in a robot- building competition for high school students.

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