Compound Inequalities

Front

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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What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' indicates that both conditions must be true simultaneously.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' indicates that at least one of the conditions must be true.

Front

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

Back

To graph a compound inequality with 'and', find the intersection of the two inequalities on a number line.

Front

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

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To graph a compound inequality with 'or', find the union of the two inequalities on a number line.

Front

What is the solution to the compound inequality x < 3 and x > 1?

Back

The solution is 1 < x < 3.

Front

What is the solution to the compound inequality x ≤ -2 or x > 5?

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

Front

How do you solve the inequality 2.50x + 5 ≤ 20?

Back

Subtract 5 from both sides to get 2.50x ≤ 15, then divide by 2.50 to find x ≤ 6.

Front

What is the first step in solving a compound inequality?

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Identify whether the compound inequality uses 'and' or 'or' to determine how to approach the solution.

Front

What is an example of a real-world scenario that can be modeled with a compound inequality?

Back

A budget constraint for spending on multiple items, such as a taxi fare combined with a maximum budget.