Algebra II Inequalities Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '|' represent in absolute value inequalities?

Back

The symbol '|' represents the absolute value, which measures the distance of a number from zero on the number line, regardless of direction.

Front

How do you solve an absolute value inequality like |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

Front

What does an open interval (a, b) mean?

Back

An open interval (a, b) includes all numbers between a and b but does not include the endpoints a and b.

Front

What does a closed interval [a, b] mean?

Back

A closed interval [a, b] includes all numbers between a and b, including the endpoints a and b.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the endpoints, while non-strict inequalities (≤, ≥) do include the endpoints.

Front

How do you graph the inequality x < 3?

Back

To graph x < 3, draw a number line, place an open circle at 3, and shade to the left.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that satisfy the inequality, such as 3 | 2x + 7| + 7 < 4.

Front

Can you use brackets [ ] with infinity in interval notation?

Back

No, you cannot use brackets [ ] with infinity; you must use parentheses ( ).