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 > 2 or x ≤ -3' represent on a number line?

Back

It represents all values of x that are greater than 2 or less than or equal to -3, with shading that points away from the intersection.

Front

What does 'x ≥ 2 and x ≤ 4' mean?

Back

It means x is between 2 and 4, inclusive, meaning x can equal 2 or 4.

Front

How do you graph 'x > 2 or x < -3'?

Back

You graph two separate regions: one for x > 2 (open circle at 2, shading to the right) and one for x < -3 (open circle at -3, shading to the left).

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 condition must be true.

Front

What does the symbol '<' represent?

Back

The symbol '<' means 'less than'.

Front

How do you represent 'x < 5' on a number line?

Back

You place an open circle at 5 and shade to the left.

Front

What does '0 ≤ x < 5' indicate?

Back

It indicates that x can be 0 or any value less than 5, but not including 5.

Front

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

Back

It is represented by a line segment between 2 and 4, with open circles at both ends.

Front

What does the term 'solution set' refer to in inequalities?

Back

The solution set is the set of all values that satisfy the inequality.