Linear Inequalities / Systems of Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

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What does the symbol '≥' indicate in a linear inequality?

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The symbol '≥' indicates that the value on the left side of the inequality is greater than or equal to the value on the right side.

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What does the symbol '≤' indicate in a linear inequality?

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The symbol '≤' indicates that the value on the left side of the inequality is less than or equal to the value on the right side.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered simultaneously.

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How do you determine the solution set of a system of linear inequalities?

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The solution set is the region where the shaded areas of all inequalities overlap on the graph.

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What does it mean if a point lies on the boundary line of an inequality?

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If a point lies on the boundary line of an inequality, it is included in the solution set if the inequality is ≤ or ≥, but not included if the inequality is < or >.

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Graph both inequalities, using a solid line for the first and a dashed line for the second. The solution is the region where the shaded areas overlap.