11-20 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 of a linear inequality represent?

Back

The solution of a linear inequality represents all the values that satisfy the inequality, often visualized as a region on a graph.

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 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 they are not included (> or <).

Front

What does the inequality y ≤ 3x represent graphically?

Back

It represents all points on or below the line y = 3x.

Front

What is the significance of the inequality symbol in a linear inequality?

Back

The inequality symbol indicates the relationship between two expressions, determining whether one is greater than, less than, or equal to the other.

Front

How can you graph the inequality 5 ≥ x?

Back

Graph the line x = 5 as a solid line and shade to the left to indicate all values less than or equal to 5.

Front

What does the solution set of a system of inequalities represent?

Back

The solution set represents all points that satisfy all inequalities in the system simultaneously.

Front

How do you find the intersection of two inequalities?

Back

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

Front

What is a system of inequalities?

Back

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