Compound Inequalities

Front

Define compound inequality.

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'. For example, x < 5 and x > 1.

Front

What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' indicates that both conditions must be true simultaneously. For example, x > 1 and x < 5 means x must be greater than 1 and less than 5.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' indicates that at least one of the conditions must be true. For example, x < 1 or x > 5 means x can be less than 1 or greater than 5.

Front

Solve the compound inequality: 0 < x + 7 < 9.

Back

-7 < x < 2.

Front

Solve the compound inequality: 3x + 2 < -7 or -4x + 5 < 1.

Back

x < -3 or x > 1.

Front

What is the solution set for the inequality 5(v + 3) - 10v > -10?

Back

v < 5.

Front

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

Back

Graph the solution of each inequality on the same number line and find the overlap (intersection) of the two solutions.

Front

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

Back

Graph the solution of each inequality on the same number line and combine the two solutions (union) to show all possible values.

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

Solve the inequality: 2x - 3 < 5 and x + 4 > 2.

Back

x < 4 and x > -2.