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

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve a compound inequality that uses 'and'?

Back

To solve a compound inequality that uses 'and', you find the intersection of the solution sets of the individual inequalities.

Front

How do you solve a compound inequality that uses 'or'?

Back

To solve a compound inequality that uses 'or', you find the union of the solution sets of the individual inequalities.

Front

What is the solution set for the inequality 6 < x + 5 ≤ 11?

Back

The solution set is 1 < x ≤ 6.

Front

How can you represent the inequality 'x is greater than 5' in interval notation?

Back

In interval notation, it is represented as (5, ∞).

Front

What does the phrase 'no more than' indicate in an inequality?

Back

The phrase 'no more than' indicates that the value is less than or equal to a certain number, represented by '≤'.

Front

What is the graphical representation of the inequality x ≤ -2?

Back

The graphical representation is a solid dot at -2 and a line extending to the left.

Front

How do you express the inequality 'p is less than 9' in mathematical terms?

Back

It is expressed as p < 9.

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.