Linear Inequalities and 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 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 linear inequality?

Back

Yes, they are part of the solution set if the inequality is inclusive (≥ or ≤).

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 set (≥ or ≤), while a dashed line indicates they 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 does the shading in the graph of a linear inequality represent?

Back

The shading represents the region of the graph that contains all the solutions to the inequality.

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 and identify the region where the shaded areas overlap.

Front

What is the significance of the intersection of the shaded regions in a system of linear inequalities?

Back

The intersection represents the set of solutions that satisfy all inequalities in the system.

Front

What is the solution to the inequality y ≥ 4x - 5 for the point (1, 1)?

Back

Substituting (1, 1) gives 1 ≥ 4(1) - 5, which simplifies to 1 ≥ -1. This is true, so (1, 1) is a solution.