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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 '>' represent in inequalities?

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The symbol '>' means 'greater than' and indicates that the value on the left side of the inequality is larger than the value on the right side.

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What does the symbol '<' represent in inequalities?

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The symbol '<' means 'less than' and indicates that the value on the left side of the inequality is smaller than the value on the right side.

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What is the solution set of an inequality?

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The solution set of an inequality is the set of all values that satisfy the inequality.

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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 boundary line. Then, shade the region that satisfies the inequality.

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What is the difference between 'greater than' and 'greater than or equal to'?

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'Greater than' (>) does not include the boundary value, while 'greater than or equal to' (≥) includes the boundary value.

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What is the significance of the boundary line in a linear inequality?

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The boundary line represents the values where the inequality changes from true to false. It is dashed for 'greater than' or 'less than' and solid for 'greater than or equal to' or 'less than or equal to'.

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What does it mean if an inequality has no solution?

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An inequality has no solution when there are no values that can satisfy the inequality, often resulting from contradictory statements.

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What is a system of inequalities?

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A system of inequalities consists of two or more inequalities that are considered simultaneously, and the solution is the region where all inequalities overlap.