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What is a linear inequality?

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

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.

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What does a dashed line indicate in a graph of a linear inequality?

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A dashed line indicates that the points on the line are not included in the solution set (for inequalities like < or >).

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What does a solid line indicate in a graph of a linear inequality?

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A solid line indicates that the points on the line are included in the solution set (for inequalities like ≤ or ≥).

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How can you tell if an inequality will have a dashed line?

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An inequality will have a dashed line if it does not include 'or equal to' (i.e., it uses < or >).

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How can you tell if an inequality will have a solid line?

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An inequality will have a solid line if it includes 'or equal to' (i.e., it uses ≤ or ≥).

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What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

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

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The symbol '≤' means 'less than or equal to', indicating that the values on the line are included in the solution set.

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

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The symbol '≥' means 'greater than or equal to', indicating that the values on the line are included in the solution set.

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How do you determine which side of the line to shade when graphing a linear inequality?

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To determine which side to shade, pick a test point (usually (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.