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 'AND' mean in compound inequalities?

Back

In compound inequalities, 'AND' indicates that both conditions must be true simultaneously.

Front

What does 'OR' mean in compound inequalities?

Back

In compound inequalities, 'OR' indicates that at least one of the conditions must be true.

Front

How do you represent the inequality for the graph showing x ≤ -2 OR x > 5?

Back

The inequality is represented as x ≤ -2 OR x > 5.

Front

Solve the compound inequality: x + 2 < -4 or -5x < -15.

Back

The solution is x < -6 or x > 3.

Front

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

Back

The solution set is 2 ≤ x ≤ 4.

Front

How do you solve the compound inequality 2 < x + 2 < 5?

Back

Subtract 2 from all parts to get 0 < x < 3.

Front

What is the graphical representation of x > 2 and x < 4?

Back

The graph shows a line between 2 and 4, not including the endpoints.

Front

What is the difference between 'x < 5' and 'x ≤ 5'?

Back

'x < 5' means x can be any number less than 5, while 'x ≤ 5' includes 5.

Front

What does it mean if a compound inequality has no solution?

Back

It means there are no values that satisfy both conditions of the inequality.