#65 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 'or' mean in a compound inequality?

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In a compound inequality, 'or' indicates that at least one of the inequalities must be true for the solution to be valid.

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What does 'and' mean in a compound inequality?

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In a compound inequality, 'and' indicates that both inequalities must be true for the solution to be valid.

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

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To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

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

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To solve a compound inequality with 'and', solve each inequality separately and find the intersection of the solutions.

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What is the solution to the inequality: -8 < 2(x + 4) or -3x + 4 > x - 4?

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x > -8 or x < 2.

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

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-8 < r < 3.

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What is the solution to the inequality: -3 ≤ 2x - 1 ≤ 5?

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-1 ≤ x ≤ 3.

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What is the solution to the inequality: 3x + 2 < -4 or 4x + 4 > 24?

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x < -2 or x > 5.

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What is the first step in solving a compound inequality?

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Identify whether the compound inequality uses 'and' or 'or' and separate the inequalities accordingly.