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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality.

Front

What is the difference between '>' and '≥' in linear inequalities?

Back

'>' means that the boundary line is not included in the solution set, while '≥' means the boundary line is included.

Front

What does it mean if a point is a solution to a system of linear inequalities?

Back

A point is a solution to a system of linear inequalities if it satisfies all inequalities in the system.

Front

How can you determine if a point is part of the solution set for a linear inequality?

Back

Substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the graphical representation of the inequality y < 2x - 4?

Back

The graph will have a dashed line for y = 2x - 4, and the area below the line will be shaded.

Front

What does the term 'system of inequalities' refer to?

Back

A system of inequalities is a set of two or more inequalities with the same variables.

Front

How do you find the intersection of two linear inequalities?

Back

Graph both inequalities and identify the region where the shaded areas overlap; this region represents the intersection.

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 where the inequality changes.