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

Solve the compound inequality: -3 ≤ 2x - 1 ≤ 5.

Back

-1 ≤ x ≤ 3.

Front

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

Back

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

Front

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

Back

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

Front

Solve the compound inequality: 2x + 1 > 9 or x - 4 < 6.

Back

All real numbers.

Front

Which of the following results in no solution: x < 1 and x > 5?

Back

This compound inequality has no solution because no number can be both less than 1 and greater than 5.

Front

What is the solution set for the inequality: 2 ≤ x ≤ 4?

Back

The solution set is all numbers x such that x is greater than or equal to 2 and less than or equal to 4.

Front

How do you graph the compound inequality x > 2 and x < 4?

Back

You would draw a number line and shade the region between 2 and 4, using open circles at 2 and 4.

Front

What is the difference between 'x < 1 or x > 5' and 'x < 1 and x > 5'?

Back

'x < 1 or x > 5' has solutions outside the interval [1, 5], while 'x < 1 and x > 5' has no solutions.

Front

If x - 3 < 2 or x + 1 > 5, what is the solution set?

Back

The solution set is all real numbers.