Compound Inequalities

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What is a compound inequality?

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A compound inequality is an inequality that combines two simple inequalities using the words 'and' or 'or'. For example, -2 < x < 3 is a compound inequality.

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How do you graph the compound inequality -2 < x < 3?

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To graph -2 < x < 3, draw a number line, place open circles at -2 and 3, and shade the region between them.

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What does the symbol '<' mean in inequalities?

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The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

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What does the symbol '≤' mean in inequalities?

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The symbol '≤' means 'less than or equal to'. For example, x ≤ 3 means x can be any number less than or equal to 3.

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What does the symbol '>' mean in inequalities?

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The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

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What does the symbol '≥' mean in inequalities?

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The symbol '≥' means 'greater than or equal to'. For example, x ≥ 3 means x can be any number greater than or equal to 3.

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How do you solve the compound inequality 0 < x ≤ 3?

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To solve 0 < x ≤ 3, x must be greater than 0 and less than or equal to 3. The solution is the interval (0, 3].

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What is the solution set for the inequality x < 3?

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The solution set for x < 3 includes all real numbers less than 3.

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What is the solution set for the inequality -2 ≤ x ≤ 3?

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The solution set for -2 ≤ x ≤ 3 includes all real numbers from -2 to 3, including -2 and 3.

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What does it mean if a graph has an open circle at a number?

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An open circle indicates that the number is not included in the solution set. For example, x < 3 has an open circle at 3.