Solutions to Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

What does a dashed line represent in a graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set.

Front

What does a solid line represent in a graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set.

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the solution set of a linear inequality?

Back

The solution set is the set of all points that satisfy the inequality, often represented as a shaded region on a graph.

Front

What does it mean if a point lies in the shaded region of a graph of a linear inequality?

Back

It means that the point is a solution to the inequality.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the solution set from the non-solution set.

Front

Can a point on a dashed line be part of the solution set?

Back

No, points on a dashed line are not part of the solution set.

Front

Can a point on a solid line be part of the solution set?

Back

Yes, points on a solid line are included in the solution set.

Front

What is the graphical representation of the inequality y < 2x + 3?

Back

The graph will have a dashed line for y = 2x + 3, and the area below the line will be shaded.