Compound Inequalities and Interval Notation

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'.

Front

What does 'or' mean in compound inequalities?

Back

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

Front

What does 'and' mean in compound inequalities?

Back

In compound inequalities, 'and' means that both inequalities must be true simultaneously.

Front

How do you solve the compound inequality 3x + 2 < -7 or -4x + 5 < 1?

Back

x < -3 or x > 1.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals.

Front

How is the interval [-4, -1) interpreted?

Back

It includes -4 and goes up to, but does not include, -1.

Front

What does the notation (a, b) represent?

Back

It represents an open interval that does not include the endpoints a and b.

Front

What does the notation [a, b] represent?

Back

It represents a closed interval that includes both endpoints a and b.

Front

How do you express the solution -1 ≤ x ≤ 3 in interval notation?

Back

The interval notation is [-1, 3].

Front

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

Back

The solution is -1 ≤ x ≤ 3.