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 graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of the boundary line.

Front

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

Back

A solid line indicates that points on the line are included in the solution (≥ 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 a system of linear inequalities?

Back

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

Front

How do you graph a system of linear inequalities?

Back

Graph each inequality on the same coordinate plane, using solid or dashed lines as appropriate, and shade the solution regions. The solution set is where the shaded areas overlap.

Front

What does it mean for a point to be part of the solution set of a system of inequalities?

Back

A point is part of the solution set if it satisfies all inequalities in the system.

Front

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

Back

The boundary line separates the coordinate plane into two regions: one that contains the solutions to the inequality and one that does not.

Front

How can you tell which side of the boundary line to shade?

Back

You can test a point not on the line (often (0,0) if it's not on the line) in the inequality. If the inequality is true, shade the side containing that point.

Front

What is the solution to the inequality y < 2x + 3?

Back

The solution is the region below the line y = 2x + 3, with a dashed line indicating that points on the line are not included.