Linear Inequalities

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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 (>, <, ≥, ≤).

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

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

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

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

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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'. It indicates that the value on the left side is either larger than or equal to the value on the right.

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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'. It indicates that the value on the left side is either smaller than or equal to the value on the right.

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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 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 happens to the inequality sign when you multiply or divide by a negative number?

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When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

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