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

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

Front

What does the solution x < -6 or x > 3 represent on a number line?

Back

It represents two separate regions: all numbers less than -6 and all numbers greater than 3.

Front

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

Back

'And' requires both conditions to be true simultaneously, while 'or' allows for either condition to be true.

Front

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

Back

Graph a dashed line at x = 2 with shading to the right, and a solid line at x = -3 with shading to the left.

Front

What is the solution to the compound inequality -3 < 3x < 6?

Back

Divide all parts by 3 to get -1 < x < 2.

Front

How do you write an inequality for a graph that shows -2 ≤ x ≤ 5?

Back

The inequality is written as -2 ≤ x ≤ 5, indicating that x includes -2 and 5.

Front

What does the notation 'x ≤ -3' indicate?

Back

It indicates that x can be any number less than or equal to -3.

Front

How do you solve the inequality -5x < -15?

Back

Divide both sides by -5, remembering to reverse the inequality sign, resulting in x > 3.

Front

What is the graphical representation of the inequality x < -6?

Back

A solid line at -6 with shading to the left, indicating all numbers less than -6.