12.10 Solving Multi-step Inequalities

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What is a multi-step inequality?

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A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

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How do you isolate a variable in an inequality?

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To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

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

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An inequality has all real numbers as a solution when any value substituted into the inequality makes it true, indicating that the inequality is always satisfied.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) include the boundary points.