Solving 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 'x ≤ 12' mean?

Back

It means that x can be any number less than or equal to 12.

Front

How do you solve the compound inequality '6 < x + 5 ≤ 11'?

Back

First, solve the left part: 6 < x + 5 gives x > 1. Then solve the right part: x + 5 ≤ 11 gives x ≤ 6. The solution is 1 < x ≤ 6.

Front

What is the solution to the inequality 'p < 9'?

Back

The solution includes all values of p that are less than 9.

Front

What does 'x < -8 or x < 2' represent?

Back

It means that x can be any number less than -8 or any number less than 2.

Front

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

Back

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

Front

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

Back

Shade the region to the left of -2 and the region to the right of 5 on a number line.

Front

What does the inequality 'p ≤ 9' indicate?

Back

It indicates that p can be any number that is less than or equal to 9.

Front

Can x = 3 be a solution to the inequality '6 < x + 5 ≤ 11'?

Back

Yes, because when you substitute x = 3, it satisfies both parts of the inequality.

Front

What is the solution set for 'x < -8 and x < 2'?

Back

The solution set is x < -8, since it is more restrictive.