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 of the form a < x < b?

Back

To solve a compound inequality of the form a < x < b, you find the values of x that satisfy both inequalities simultaneously.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'.

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What does the symbol '≥' mean in an inequality?

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The symbol '≥' means 'greater than or equal to'.

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How do you graph the inequality -2 ≤ x ≤ 5?

Back

To graph -2 ≤ x ≤ 5, draw a solid dot at -2 and 5, and shade the region between them.

Front

What is the solution to the compound inequality 0 < x + 7 < 9?

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The solution is -7 < x < 2.

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What does the word 'or' indicate in a compound inequality?

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The word 'or' indicates that at least one of the inequalities must be true.

Front

What does the word 'and' indicate in a compound inequality?

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The word 'and' indicates that both inequalities must be true at the same time.

Front

How do you write an inequality for the graph that shows x < -2 or x > 5?

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The inequality is x < -2 or x > 5.

Front

What is the solution to the compound inequality x ≥ -2 OR x < 5?

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The solution includes all values of x that are either greater than or equal to -2 or less than 5.