Solving 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 (>, <, ≥, ≤) instead of an equal sign.

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What does it mean to solve a linear inequality?

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To solve a linear inequality means to find all values of the variable that make the inequality true.

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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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What is the difference between a linear equation and a linear inequality?

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A linear equation states that two expressions are equal, while a linear inequality states that one expression is greater than or less than another.

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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 region that represents the solution set.

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What does it mean if an inequality has no solution?

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An inequality has no solution if there are no values that satisfy the inequality, often resulting from a contradiction.

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What does it mean if an inequality has all real numbers as a solution?

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If an inequality has all real numbers as a solution, it means that any value of the variable will satisfy the inequality.

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How do you isolate a variable in a linear inequality?

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To isolate a variable in a linear inequality, use inverse operations to get the variable on one side of the inequality.

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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 reverse the inequality sign.

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All real numbers.