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, divide the entire inequality by -3 (remember to reverse the inequality signs): -8 < r < 3.

Front

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

Back

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

Front

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

Back

The inequality is x ≤ -2 OR x > 5.

Front

What is the solution to the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

The solution is x ≥ -5 and x < 4.

Front

How do you express the solution x ≥ -5 and x < 4 in interval notation?

Back

The interval notation is [-5, 4).

Front

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

Back

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

Front

What is the graphical representation of x ≤ -2 OR x > 5?

Back

The graph shows a closed circle at -2 extending to the left and an open circle at 5 extending to the right.