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 to reverse the inequality sign?

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Reversing the inequality sign means changing '<' to '>' or '≤' to '≥' (and vice versa) when you multiply or divide both sides of the inequality by a negative number.

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How do you graph the solution of an inequality on a number line?

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To graph the solution of an inequality, draw a number line, use an open circle for '<' or '>' (not including the endpoint) and a closed circle for '≤' or '≥' (including the endpoint), and shade the appropriate direction.

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What is the difference between a strict and non-strict inequality?

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A strict inequality (e.g., '<' or '>') does not include the endpoint, while a non-strict inequality (e.g., '≤' or '≥') includes the endpoint.

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What is a compound inequality?

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A compound inequality consists of two or more inequalities joined by 'and' or 'or', representing a range of values.