Solve and Graph 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 notation {x | x < 4} represent?

Back

It represents the set of all x values that are less than 4.

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

How do you graph the inequality x < 4?

Back

You draw a number line, shade to the left of 4, and use an open circle at 4 to indicate that 4 is not included.

Front

What does the interval (-∞, 4) mean?

Back

It represents all real numbers less than 4, extending indefinitely to the left.

Front

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

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.

Front

How do you solve the compound inequality x < 4 and x > 2?

Back

The solution is the interval (2, 4), meaning x is greater than 2 and less than 4.

Front

What is the solution to the compound inequality x < 4 or x > 6?

Back

The solution is the union of the intervals (-∞, 4) and (6, ∞).

Front

What does the graph of x > 6 look like?

Back

It is represented by a number line with a closed circle at 6 and shading to the right.

Front

How do you express the solution of x < 4 in interval notation?

Back

The solution in interval notation is (-∞, 4).