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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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, represented graphically as a shaded region on the graph.

Tags

CCSS.HSA.REI.D.12

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

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the inequality symbol in a linear inequality?

Back

The inequality symbol indicates the relationship between the two expressions, determining whether the solution set includes or excludes certain points.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

First, graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality.

Tags

CCSS.HSA.REI.D.12