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 the 'and' in a compound inequality signify?

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The 'and' in a compound inequality signifies that both conditions must be true simultaneously.

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What does the 'or' in a compound inequality signify?

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The 'or' in a compound inequality signifies 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', solve each inequality separately and find the intersection of the solutions.

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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 find the union of the solutions.

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What is the solution to the inequality 3x - 4 < -13?

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The solution is x < -3.

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What is the solution to the inequality 7x + 1 > 22?

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The solution is x > 3.

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How do you express the solution of a compound inequality graphically?

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The solution of a compound inequality can be expressed graphically on a number line, showing the ranges of values that satisfy the inequalities.

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

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The solution is x ≥ -5 and x < 4.

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How do you write an inequality based on a graph?

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To write an inequality based on a graph, identify the endpoints and whether the intervals are open or closed, then express it in inequality notation.