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'. It indicates that the value on the left side of the symbol is larger than the value on the right side.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the symbol is smaller than the value on the right side.

Front

What does a closed circle represent when graphing inequalities?

Back

A closed circle indicates that the number is included in the solution set of the inequality.

Front

What does an open circle represent when graphing inequalities?

Back

An open circle indicates that the number is not included in the solution set of the inequality.

Front

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

Back

Subtract 5 from both sides: x > 2.

Front

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

Back

The inequality symbol flips (e.g., > becomes < and vice versa).

Front

Write the inequality for a limo driver who needs to make more than $450 if he charges $375 and $0.85 per mile.

Back

0.85x + 375 > 450.

Front

What is the first step to solve the inequality 0.85x + 375 > 450?

Back

Subtract 375 from both sides: 0.85x > 75.

Front

How do you isolate x in the inequality 0.85x > 75?

Back

Divide both sides by 0.85: x > 88.24.