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 inequality 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 inequality is smaller than the value on the right side.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either greater than or equal to the value on the right side.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either less than or equal to the value on the right side.

Front

How do you solve the inequality 4x + 6 > 22?

Back

Subtract 6 from both sides: 4x > 16. Then divide by 4: x > 4.

Front

What is the solution to the inequality -4 - 6m > -9m + 8?

Back

Rearranging gives m > 4.

Front

How do you graph the inequality x + 5 ≤ 13?

Back

First, solve for x: x ≤ 8. Then, graph a closed circle at 8 and shade to the left.

Front

What does a closed circle mean when graphing inequalities?

Back

A closed circle means that the number is included in the solution set.

Front

What does an open circle mean when graphing inequalities?

Back

An open circle means that the number is not included in the solution set.