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 and x ≤ 4' represent on a number line?

Back

It represents all numbers between 2 and 4, including 2 and 4.

Front

How do you solve the compound inequality -3 < 3x < 6?

Back

Divide all parts by 3: -1 < x < 2.

Front

What does 'x ≤ -2 OR x > 5' mean?

Back

It means x can be any number less than or equal to -2 or any number greater than 5.

Front

What is the solution to the inequality x + 2 < -4?

Back

x < -6.

Front

How do you graph the inequality x < -6?

Back

Draw a number line, place an open circle at -6, and shade to the left.

Front

What does the inequality -2 < x - 9 < 3 represent?

Back

It represents the range of x values that are greater than -2 and less than 12.

Front

What is the solution to the compound inequality -5x < -15?

Back

x > 3.

Front

What does 'x < 12' indicate in terms of x values?

Back

It indicates that x can be any number less than 12.

Front

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

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.