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 the symbol 'or' indicate in compound inequalities?

Back

The symbol 'or' indicates that at least one of the inequalities must be true.

Front

What does the symbol 'and' indicate in compound inequalities?

Back

The symbol 'and' indicates that both inequalities must be true at the same time.

Front

How do you express the compound inequality x > 2 or x ≤ -3 in interval notation?

Back

(-∞, -3] ∪ (2, ∞)

Front

Can you use the symbols [ or ] with infinity?

Back

No, you cannot use brackets with infinity; you must use parentheses.

Front

What is the solution set for the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

The solution set is -1 ≤ x ≤ 3.

Front

How do you express the compound inequality -2 ≤ x ≤ 5 in interval notation?

Back

[-2, 5]

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include endpoints (e.g., (a, b)), while closed intervals do include endpoints (e.g., [a, b]).

Front

What is the solution to the 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.