Compound Inequalities answers

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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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It represents all values of x that are greater than 1.

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It means that x can be any value less than or equal to 2.

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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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How do you express the compound inequality 'x is less than or equal to 1 or x is greater than 4' in interval notation?

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The interval notation is (-∞, 1] ∪ (4, ∞).

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It indicates that x can take any value from 9 to 13, inclusive.

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

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'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

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How do you write the solution for the compound inequality 'x < 2 and x > -1' in interval notation?

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The interval notation is (-1, 2).

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It implies that x can be any value greater than 6 or any value less than 8.

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What is the solution set for the compound inequality 'x < 1 or x > 4'?

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The solution set is all real numbers except for the interval [1, 4].