1E Compound Inequalities 3

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 > 5' represent on a number line?

Back

It represents all values of x that are either less than -2 or greater than 5, with open intervals on both ends.

Front

What does '2 ≤ x ≤ 4' mean?

Back

It means x is greater than or equal to 2 and less than or equal to 4, including the endpoints.

Front

When do you use an open dot on a graph?

Back

An open dot is used when the inequality symbol is '<' or '>', indicating that the endpoint is not included.

Front

What does 'x > 2 or x ≤ -3' indicate?

Back

It indicates that x can be any value greater than 2 or any value less than or equal to -3.

Front

How do you graph 'x < -2'?

Back

You draw a number line, place an open dot at -2, and shade 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 inequality '-2 < x ≤ 2' look like on a number line?

Back

It has an open dot at -2, a closed dot at 2, and shading between -2 and 2.

Front

What is the solution set for 'x > 2 and x < 4'?

Back

The solution set is the interval (2, 4), meaning x can take any value between 2 and 4, not including the endpoints.

Front

How do you represent 'x ≤ -3' on a graph?

Back

You place a closed dot at -3 and shade to the left.