Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) to show that one expression is greater than, less than, or equal to another.

Front

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

Back

The symbol '>' means 'greater than'. For example, x > 2 means x is greater than 2.

Front

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

Back

The symbol '<' means 'less than'. For example, x < 5 means x is less than 5.

Front

What does a closed circle mean when graphing an inequality?

Back

A closed circle means that the number is included in the solution set. For example, x ≤ 3 is represented with a closed circle at 3.

Front

What does an open circle mean when graphing an inequality?

Back

An open circle means that the number is not included in the solution set. For example, x < 3 is represented with an open circle at 3.

Front

How do you solve the inequality x + 5 > 7?

Back

Subtract 5 from both sides: x > 2.

Front

What is the first step to solve the inequality 12y < 120?

Back

Divide both sides by 12: y < 10.

Front

What happens to the inequality symbol when you multiply or divide by a negative number?

Back

You must flip the inequality symbol. For example, if -2x > 6, dividing by -2 gives x < -3.

Front

What inequality represents the situation: A limo driver needs to make more than $450 in one day with a rental fee of $375 and $0.85 per mile?

Back

0.85x + 375 > 450.

Front

What is the solution to the inequality 0.85x + 375 > 450?

Back

Subtract 375 from both sides: 0.85x > 75, then divide by 0.85: x > 88.24.