2.11 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'.

Front

What does the inequality x > 2 represent on a number line?

Back

It represents all numbers greater than 2, which is shown as an open circle at 2 and a line extending to the right.

Front

What does the inequality x ≤ -3 represent on a number line?

Back

It represents all numbers less than or equal to -3, which is shown as a closed circle at -3 and a line extending to the left.

Front

How do you solve the compound inequality x > 2 or x ≤ -3?

Back

You solve each part separately: x > 2 means all numbers greater than 2, and x ≤ -3 means all numbers less than or equal to -3.

Front

What is the solution set for the compound inequality -2 ≤ x ≤ 5?

Back

The solution set includes all numbers from -2 to 5, including -2 and 5.

Front

How do you translate the phrase 'four times a number increased by 6 is greater than 22' into an inequality?

Back

The phrase translates to the inequality 4x + 6 > 22.

Front

What is the solution to the inequality 4x + 6 > 22?

Back

To solve, subtract 6 from both sides to get 4x > 16, then divide by 4 to find x > 4.

Front

How do you solve the double inequality 0 < x + 7 < 9?

Back

First, subtract 7 from all parts to get -7 < x < 2.

Front

What does the inequality 2 ≤ x ≤ 4 represent?

Back

It represents all numbers x that are greater than or equal to 2 and less than or equal to 4.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.