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

What is the solution to the compound inequality x < 1 and x > 5?

Back

There is no solution because no number can be both less than 1 and greater than 5.

Front

How do you express the compound inequality -8 ≤ x < 8 in interval notation?

Back

The interval notation is [-8, 8).

Front

What is the graph of the inequality x > 2 or x ≤ -3?

Back

The graph consists of two separate regions: one to the right of 2 (not including 2) and one to the left of -3 (including -3).

Front

What is the solution to the compound inequality x < -2 or x > 5?

Back

The solution in interval notation is (-∞, -2) ∪ (5, ∞).

Front

How do you solve the compound inequality 3 < x + 2 < 7?

Back

Subtract 2 from all parts: 1 < x < 5. The solution in interval notation is (1, 5).

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

How do you graph the compound inequality x ≤ 4 and x > 1?

Back

Shade the region between 1 and 4, including 4 but not including 1.