Solving 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

How do you solve the compound inequality |6n| ≤ 18?

Back

The solution is -3 ≤ n ≤ 3.

Front

What does the solution set {-6, 5} represent in the context of inequalities?

Back

It represents two specific values of 'r' that satisfy the equation -|−2r − 1| = 11.

Front

What is the solution to the equation |2x + 9| = 15?

Back

The solutions are x = 3 and x = -12.

Front

How do you determine if a value is a solution to an inequality?

Back

Substitute the value into the inequality and check if the statement is true.

Front

What is the solution to the compound inequality x + 8 < 3 or -8x < -40?

Back

The solution is x < -5 or x > 5.

Front

What does the term 'absolute value' mean?

Back

Absolute value refers to the distance of a number from zero on the number line, regardless of direction.

Front

What is the significance of the 'and' in compound inequalities?

Back

The 'and' indicates that both inequalities must be true at the same time.

Front

What is the significance of the 'or' in compound inequalities?

Back

The 'or' indicates that at least one of the inequalities must be true.

Front

How do you graph a compound inequality?

Back

Graph each inequality on the number line and combine the solutions based on 'and' or 'or'.