Introduction to Inequalities Practice - A

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '>' represent in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is greater than 3.

Front

What does the symbol '<' represent in inequalities?

Back

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

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 3 means x is greater than or equal to 3.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 3 means x is less than or equal to 3.

Front

How do you graph the inequality x < 3?

Back

To graph x < 3, draw a number line, place an open circle at 3, and shade to the left to indicate all numbers less than 3.

Front

How do you graph the inequality x ≥ -5?

Back

To graph x ≥ -5, draw a number line, place a closed circle at -5, and shade to the right to indicate all numbers greater than or equal to -5.

Front

What is the difference between an open circle and a closed circle in graphing inequalities?

Back

An open circle indicates that the number is not included in the solution (e.g., x < 3), while a closed circle indicates that the number is included (e.g., x ≥ -5).

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, such as x > 1 and x < 5, which can be written as 1 < x < 5.

Front

How do you solve the inequality 2x + 3 < 7?

Back

To solve 2x + 3 < 7, subtract 3 from both sides to get 2x < 4, then divide by 2 to find x < 2.