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 (>, <, ≥, ≤).

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

Front

Are the points on the boundary line part of the solution set for a '≥' or '≤' inequality?

Back

Yes, the points on the boundary line are part of the solution set for '≥' or '≤' inequalities.

Front

Are the points on the boundary line part of the solution set for a '>' or '<' inequality?

Back

No, the points on the boundary line are NOT part of the solution set for '>' or '<' inequalities.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a shaded region on one side of the boundary line, indicating all the solutions.

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 (for '>' or '<' inequalities).

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 (for '≥' or '≤' inequalities).

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 point's coordinates into the inequality and check if the statement is true.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that are considered together.

Front

How do you graph a system of linear inequalities?

Back

Graph each inequality on the same coordinate plane and identify the overlapping shaded region as the solution set.