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 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 set (≥ 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 into the inequality. If the inequality holds true, the point is a solution.

Front

What does the solution set of a linear inequality look like?

Back

The solution set of a linear inequality is represented by a shaded region on the graph, indicating all the points that satisfy the inequality.

Front

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

Back

The boundary line separates the solution set from the non-solution set and indicates the relationship defined by the inequality.

Front

How can you graph the inequality y ≤ 2/5x + 1?

Back

Graph the line y = 2/5x + 1 as a solid line and shade below the line to represent all points where y is less than or equal to the line.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the line is solid, and not included if the line is dashed.

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, and the solution is the region where all inequalities overlap.

Front

How do you find the solution to a system of linear inequalities?

Back

To find the solution, graph each inequality on the same coordinate plane and identify the overlapping shaded region.