Solving 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 a compound inequality?

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In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

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In a compound inequality, 'or' means 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.

Front

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.

Front

What is the solution to the inequality 6 < x + 5 ≤ 11?

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The solution is 1 < x ≤ 6.

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Can x = 3 be a solution to the inequality 6 < x + 5 ≤ 11?

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Yes, x = 3 is a solution.

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What is the solution to the compound inequality 24 > -3r > -9?

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The solution is -8 < r < 3.

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What is the solution to the compound inequality m ≤ -5 or m ≥ 0?

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The solution includes all values of m that are less than or equal to -5 or greater than or equal to 0.

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How do you graph the solution of a compound inequality?

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To graph a compound inequality, use open circles for '>' or '<' and closed circles for '≥' or '≤', and shade the appropriate regions.