12-11-24 Compound Inequalities

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What is a compound inequality?

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A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'. For example, -2 ≤ x ≤ 2 is a compound inequality.

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What does the symbol ≤ mean in an inequality?

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The symbol ≤ means 'less than or equal to'. It indicates that the value can be less than or equal to a specified number.

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What does the symbol ≥ mean in an inequality?

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The symbol ≥ means 'greater than or equal to'. It indicates that the value can be greater than or equal to a specified number.

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When do you use a closed dot on a number line?

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A closed dot is used on a number line to indicate that the endpoint is included in the solution set, which occurs with ≤ or ≥.

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What does the interval notation [-2, 5] represent?

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The interval notation [-2, 5] represents all numbers x such that -2 ≤ x ≤ 5, including the endpoints -2 and 5.

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How do you solve the compound inequality -3 < 2x + 3 ≤ 15?

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To solve -3 < 2x + 3 ≤ 15, first isolate 2x by subtracting 3 from all parts: -6 < 2x ≤ 12. Then divide by 2: -3 < x ≤ 6.

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What is the solution set for the compound inequality -2 ≤ x ≤ 2?

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The solution set for -2 ≤ x ≤ 2 includes all real numbers between -2 and 2, including -2 and 2.

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What is the difference between 'and' and 'or' in compound inequalities?

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In compound inequalities, 'and' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.

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How do you graph the compound inequality -2 ≤ x ≤ 2?

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To graph -2 ≤ x ≤ 2, draw a number line, place closed dots at -2 and 2, and shade the region between them.

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