AFDA Linear Inequalities and Systems of Linear Inequalities

Front

What is a linear inequality?

Back

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

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

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

Back

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

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, often represented graphically as a shaded region on a graph.

Front

What does it mean for a system of linear inequalities to have a solution?

Back

A system of linear inequalities has a solution if there is at least one point that satisfies all inequalities in the system simultaneously.

Front

How can you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a line, then shade the appropriate region based on the inequality symbol.

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; whether it is solid or dashed indicates if points on the line are included.

Front

What does it mean if a point lies above the boundary line in a linear inequality?

Back

If a point lies above the boundary line in a linear inequality, it means that the point satisfies the inequality if the inequality is of the form y > mx + b or y ≥ mx + b.