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 area represent when graphing linear inequalities?

Back

The shaded area represents all the solutions to the linear inequality.

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (≥ or ≤).

Front

What does a dashed line indicate in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (> 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, 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 (x, y) that satisfy the inequality.

Front

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

Back

The boundary line divides the graph into two regions: one that contains the solutions and one that does not.

Front

Can a point on the boundary line be a solution to a linear inequality?

Back

Yes, if the line is solid (≥ or ≤), the point on the boundary line is 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.

Front

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

Back

If a point is above the boundary line, it is not a solution if the inequality is less than (<) or less than or equal to (≤).