Solving 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 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

How do you solve the compound inequality 24 > -3r > -9?

Back

To solve, break it into two parts: -3r < 24 and -3r > -9. Solve each part to find -8 < r < 3.

Front

What is the solution to the inequality -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

The solution is x < -8 or x < 2.

Front

How do you write an inequality for the graph showing x ≤ -2 or x > 5?

Back

The inequality is x ≤ -2 OR x > 5.

Front

What is the solution to the inequality x + 8 < 3 or -8x < -40?

Back

The solution is x < -5 or x > 5.

Front

What does it mean if an inequality is written as x ≥ -2 OR x < 5?

Back

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

Front

How do you graph the inequality -2 ≤ x < 5?

Back

Graph a closed dot at -2 and an open dot at 5, shading the region between them.

Front

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

Back

'And' requires both conditions to be true, while 'or' requires at least one condition to be true.