Unit 2: Analyzing Linear Inequalities Fall 2024 Final Review

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 it mean for a point to be a solution to a linear inequality?

Back

A point is a solution to a linear inequality if it satisfies the inequality when the coordinates of the point are substituted into the inequality.

Front

What is the significance of a dotted line in the graph of a linear inequality?

Back

A dotted line indicates that points on the line are not included in the solution set of the inequality.

Front

What does a solid line represent in the graph of a linear inequality?

Back

A solid line indicates that points on the line are included in the solution set of the inequality.

Front

How do you determine if a point is in the solution set of a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is in the solution set.

Front

What is the general form of a linear inequality in two variables?

Back

The general form is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

How can you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a line. 2. Use a solid line for ≤ or ≥ and a dotted line for < or >. 3. Shade the region that satisfies 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 together.

Front

How do you solve a system of linear inequalities graphically?

Back

Graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What does the solution to a system of linear inequalities represent?

Back

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