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 'greater than' to 'less than' or vice versa when multiplying or dividing both sides of an inequality by a negative number.

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No Solution

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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, often represented on a number line.

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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.

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How do you graph an inequality on a number line?

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To graph an inequality on a number line, use an open circle for 'less than' or 'greater than' and a closed circle for 'less than or equal to' or 'greater than or equal to', then shade the appropriate region.