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 'x < -8 or x < 2' represent?

Back

This represents all values of x that are less than -8 or less than 2.

Front

How do you solve the compound inequality -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

First, solve each inequality separately, then combine the solutions.

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 [-8, 8) expressed in set notation?

Back

The interval [-8, 8) can be expressed in set notation as {x | -8 ≤ x < 8}.

Front

What does the graph of x > 2 or x ≤ -3 look like?

Back

It consists of two separate regions: one to the right of 2 and one to the left of -3.

Front

What is the solution to the inequality -3x + 4 > x - 4?

Back

The solution is x < -2.

Front

How do you graph the inequality x < -8 or x < 2?

Back

Shade the number line to the left of -8 and to the left of 2.

Front

What does the notation (a, b) mean in interval notation?

Back

(a, b) means all numbers between a and b, not including a and b.

Front

What does the notation [a, b] mean in interval notation?

Back

[a, b] means all numbers between a and b, including a and b.