Linear Inequalities + Systems of 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 (e.g., <, >, ≤, ≥).

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What type of line is used to represent 'y < mx + b' on a graph?

Back

A dashed line is used to represent 'y < mx + b' because the points on the line are not included in the solution set.

Front

What type of line is used to represent 'y ≥ mx + b' on a graph?

Back

A solid line is used to represent 'y ≥ mx + b' because the points on the line are included in the solution set.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the set of all points that satisfy all inequalities in the system.

Front

What does it mean if an inequality is written as 'y < -x + 3'?

Back

It means that the values of y are less than the values of -x + 3, representing a region below the line y = -x + 3.

Front

What is the graphical representation of the inequality 'x + y ≤ 4'?

Back

The area below and including the line x + y = 4 is shaded, indicating all points (x, y) that satisfy the inequality.

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

How can you identify the feasible region in a system of inequalities?

Back

The feasible region is the area where all shaded regions from the inequalities overlap on the graph.