Graphing Inequalities and Systems of Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the solutions of the inequality on a number line or coordinate plane, showing where the inequality holds true.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

Front

How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution, substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables, and the solution is the region where all inequalities overlap.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and identify the overlapping region that satisfies all inequalities.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

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

Front

What is the significance of the shaded region in the graph of an inequality?

Back

The shaded region represents all possible solutions to the inequality, indicating where the inequality is true.

Front

How can you tell if a point is in the solution set of a system of inequalities?

Back

Substitute the point into each inequality in the system. If it satisfies all inequalities, it is in the solution set.

Front

What is the first step in solving a system of inequalities by graphing?

Back

The first step is to graph each inequality separately on the same coordinate plane.