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 > 5' represent on a number line?

Back

It represents two separate regions: all values of x that are less than or equal to -2 and all values of x that are greater than 5.

Front

How do you solve the compound inequality 'x + 2 < -4 or -5x < -15'?

Back

First, solve each inequality separately: x < -6 or x > 3.

Front

What is the solution set for the compound inequality 'x ≥ -2 OR x < 5'?

Back

The solution set includes all values of x that are greater than or equal to -2 and all values less than 5.

Front

What does the symbol '≤' mean in an inequality?

Back

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

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'.

Front

How do you graph the inequality 'x < -2 or x > 5'?

Back

You shade to the left of -2 and to the right of 5 on the number line.

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 is the solution to the inequality '-2 < x < 5'?

Back

The solution is all values of x that are greater than -2 and less than 5.

Front

How do you write a compound inequality for the graph that shows x is between -2 and 5?

Back

The compound inequality is -2 < x < 5.