Graphing Inequalities 2.6

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 it mean to graph an inequality?

Back

Graphing an inequality involves representing the solutions of the inequality on a number line or coordinate plane, indicating the range of values that satisfy the inequality.

Front

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

Back

A solid line indicates that the points on the line are included in the solution set (for 'greater than or equal to' or 'less than or equal to'), while a dashed line indicates that the points on the line are not included (for 'greater than' or 'less than').

Front

How do you determine if a point is part of the solution set for an inequality?

Back

To determine if a point is part of the solution set, substitute the coordinates of the point into the inequality. If the inequality holds true, 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 values that satisfy the inequality, often represented graphically.

Front

What does it mean for a point to be outside the solution set of an inequality?

Back

A point is outside the solution set if substituting its coordinates into the inequality does not satisfy the condition of the inequality.

Front

What is a boundary line in the context of graphing inequalities?

Back

A boundary line is the line that represents the equality part of the inequality. It divides the coordinate plane into regions that represent the solution set and the non-solution set.

Front

How can you identify the correct graph for a given inequality?

Back

To identify the correct graph for an inequality, analyze the inequality's direction (greater than or less than), the type of boundary line (solid or dashed), and the region that satisfies the inequality.

Front

What is the significance of test points in graphing inequalities?

Back

Test points are used to determine which side of the boundary line represents the solution set. By substituting a test point into the inequality, you can see if it satisfies the inequality.

Front

What are the common symbols used in inequalities?

Back

The common symbols used in inequalities are: '>' (greater than), '<' (less than), '≥' (greater than or equal to), and '≤' (less than or equal to).