Introduction to Compound Inequalities Assignment

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

How do you represent a compound inequality graphically?

Back

A compound inequality is represented on a number line by shading the regions that satisfy the inequalities.

Front

What does the symbol '≤' mean?

Back

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

Front

What does the symbol '≥' mean?

Back

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

Front

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

Back

In 'and' inequalities, both conditions must be true simultaneously. In 'or' inequalities, at least one condition must be true.

Front

Write the compound inequality for the following scenario: A number is greater than 3 but less than 7.

Back

3 < x < 7.

Front

How would you express the compound inequality 5 ≤ x < 10 in words?

Back

x is greater than or equal to 5 and less than 10.

Front

What is the solution set for the compound inequality x < -2 or x ≥ 4?

Back

The solution set includes all numbers less than -2 and all numbers greater than or equal to 4.

Front

If a compound inequality is written as x > 2 and x < 5, what is the solution set?

Back

The solution set is the interval (2, 5).

Front

How do you solve the compound inequality 1 < x + 3 < 5?

Back

Subtract 3 from all parts: -2 < x < 2.