solving and graphing compound inequalities

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What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities using the words 'and' or 'or'. It represents a range of values that satisfy one or both inequalities.

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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. The solution is the union of the solutions, meaning any value that satisfies either inequality is included.

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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. The solution is the intersection of the solutions, meaning only values that satisfy both inequalities are included.

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What does the symbol '<' mean in inequalities?

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The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

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What does the symbol '>' mean in inequalities?

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The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

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What does the symbol '≤' mean in inequalities?

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The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller than or equal to the value on the right.

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What does the symbol '≥' mean in inequalities?

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The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either larger than or equal to the value on the right.

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

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To graph a compound inequality with 'or', graph each inequality separately and shade the regions that represent the solutions. The final graph includes all shaded areas.

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

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To graph a compound inequality with 'and', graph each inequality separately and find the overlapping region. Shade only the area where both inequalities are satisfied.

Front

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

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x < -2.