Compound Inequalities

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What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

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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 solution sets.

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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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What does the solution set x < -5 or x > 5 represent?

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It represents all values of x that are either less than -5 or greater than 5, indicating two separate ranges.

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What is the solution set for the inequality 2x + 1 > 9?

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The solution set is x > 4.

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What does the notation -3 ≤ 2x - 1 ≤ 5 mean?

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It means that 2x - 1 is greater than or equal to -3 and less than or equal to 5.

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How do you isolate x in the inequality -3 ≤ 2x - 1 ≤ 5?

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Add 1 to all parts of the inequality to get -2 ≤ 2x ≤ 6, then divide by 2 to find -1 ≤ x ≤ 3.

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What is the final solution set for the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

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The final solution set is x ≥ -5 and x < 4.

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What does the solution set x < -3 or x > 1 indicate?

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It indicates that x can take any value less than -3 or any value greater than 1.

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What is the first step in solving the inequality -8x < -40?

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Divide both sides by -8, remembering to reverse the inequality sign, resulting in x > 5.