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?

Back

This represents a solution set where x can be greater than 2 or less than or equal to -3.

Front

How do you solve the compound inequality 'x + 8 < 3 or -8x < -40'?

Back

First, solve each inequality separately: x < -5 or x > 5.

Front

What is the solution set for the compound inequality '-13 < 2x + 5 < 15'?

Back

The solution set is -9 < x < 5.

Front

What does 'x + 2 < -4' imply?

Back

This implies that x is less than -6.

Front

What is the solution for '-5x < -15'?

Back

The solution is x > 3.

Front

What does 'x < -6 or x > 3' mean?

Back

This means that x can be any value less than -6 or any value greater than 3.

Front

How do you graph the inequality 'x > 2 or x ≤ -3'?

Back

Graph a number line with an open circle at 2 (for x > 2) and a closed circle at -3 (for x ≤ -3), shading to the right of 2 and to the left of -3.

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 for the compound inequality 'x + 2 < -4 or -5x < -15'?

Back

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