Linear Inequalities / Systems of 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 (>, <, ≥, ≤).

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality, indicating where the inequality holds true.

Front

What is the difference between a solid line and a dotted line in the graph of linear inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dotted 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

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

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region where the shaded areas of all inequalities overlap, representing all points that satisfy all inequalities in the system.

Front

What does it mean if a system of linear inequalities has no solution?

Back

It means that there is no point that satisfies all inequalities simultaneously, often resulting in parallel lines that never intersect.

Front

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

Back

The graph will have a dotted line for y = 2x + 3, with the area below the line shaded.

Front

How can you tell if a point lies in the solution region of a system of inequalities?

Back

By testing the point in each inequality; if it satisfies all inequalities, it lies in the solution region.

Front

What is the significance of the slope in the equation of a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).

Front

What does the term 'infinite solutions' mean in the context of linear inequalities?

Back

It means that there are countless points that satisfy the inequality, often occurring when the inequalities represent the same line.