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'.

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What does 'and' mean in compound inequalities?

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In compound inequalities, 'and' indicates that both conditions must be true at the same time.

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What does 'or' mean in compound inequalities?

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In compound inequalities, 'or' indicates that at least one of the conditions must be true.

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How do you solve a compound inequality with 'and'?

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To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

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How do you solve a compound inequality with 'or'?

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To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

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What is interval notation?

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Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

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What does the notation (a, b) represent?

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The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

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What does the notation [a, b] represent?

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The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

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How do you express the solution set x < -8 or x < 2 in interval notation?

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The solution set x < -8 or x < 2 can be expressed in interval notation as (-∞, -8) ∪ (-∞, 2).

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What is the solution to the inequality -4x + 1 ≤ 21?

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The solution to the inequality -4x + 1 ≤ 21 is x ≥ -5.