Inequalities and Solution Sets

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is any number greater than or equal to 4.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

What is a solution set in the context of inequalities?

Back

A solution set is the set of all values that satisfy the inequality.

Front

What is the solution set for the inequality y > 20?

Back

The solution set is {21, 22, 23, ...} which includes all numbers greater than 20.

Front

When graphing an inequality, what does an open dot represent?

Back

An open dot represents that the number is not included in the solution set, used for < and >.

Front

When graphing an inequality, what does a closed dot represent?

Back

A closed dot represents that the number is included in the solution set, used for ≤ and ≥.

Front

What is the solution set for the inequality x ≤ 6?

Back

The solution set is {-6, 5, 0, 6} which includes all numbers less than or equal to 6.