Linear Inequalities Exit Flashcardziz

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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 (>, <, ≥, ≤). It represents a range of possible solutions on a number line or graph.

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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 solid line (for ≥ or ≤) or a dashed line (for > or <). Then, shade the region that satisfies the inequality.

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

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If a point lies on the boundary line of a linear inequality, it is part of the solution set if the inequality includes equality (≥ or ≤). If the inequality does not include equality ( > or <), the point is not part of the solution set.

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What is the difference between rational and irrational numbers?

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Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

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What is the result of adding a rational number to an irrational number?

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The sum of a rational number and an irrational number is always irrational.

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What does the symbol @@ eq@@ represent in inequalities?

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The symbol @@ eq@@ means 'not equal to' and is used to indicate that two expressions do not have the same value.

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How do you determine if a point is a solution to a linear inequality?

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To determine if a point is a solution, substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.