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

Solve: -3 ≤ 2x - 1 ≤ 5

Back

-1 ≤ x ≤ 3

Front

What does 'and' mean in compound inequalities?

Back

In compound inequalities, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in compound inequalities?

Back

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

Front

Solve: 3x + 2 < -4 or 4x + 4 > 24

Back

x < -2 or x > 5

Front

How do you graph a compound inequality with 'and'?

Back

You graph the overlapping region of the two inequalities.

Front

How do you graph a compound inequality with 'or'?

Back

You graph both inequalities and shade the regions that satisfy either inequality.

Front

Write an inequality for the graph showing the range from -2 to 5, inclusive.

Back

-2 ≤ x ≤ 5

Front

What is the solution set for the inequality x < 2 or x > 5?

Back

The solution set includes all numbers less than 2 and all numbers greater than 5.

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.