Graphing Inequalities

Front

What is an inequality in mathematics?

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 an inequality?

Back

The symbol '>' means 'greater than'.

Front

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

Back

The symbol '<' means 'less than'.

Front

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

Back

The symbol '≥' means 'greater than or equal to'.

Front

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

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. Then shade the appropriate region based on the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (for '≥' or '≤'), while a dashed line indicates that points on the line are not included (for '>' or '<').

Front

How can you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution, substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is part of the solution set.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all points that satisfy the inequality.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that can satisfy the inequality, often represented by a contradiction.