5.5 - Systems of Inequalities Word Problems

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

How do you represent 'less than' in inequality notation?

Back

The symbol for 'less than' is '<'.

Front

How do you represent 'greater than' in inequality notation?

Back

The symbol for 'greater than' is '>'.

Front

What does it mean if a variable is subject to a maximum constraint?

Back

It means that the variable cannot exceed a certain value, often represented as x ≤ maximum value.

Front

What does it mean if a variable is subject to a minimum constraint?

Back

It means that the variable must be at least a certain value, often represented as x ≥ minimum value.

Front

How do you write an inequality for a situation where a person can complete a task in a limited amount of time?

Back

You can express it as: time per task × number of tasks ≤ total available time.

Front

What is the significance of the solution to a system of inequalities?

Back

The solution represents all possible combinations of the variables that satisfy all inequalities in the system.

Front

How do you graph a system of inequalities?

Back

You graph each inequality on the same coordinate plane and shade the region that satisfies all inequalities.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the boundary, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary.

Front

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

Back

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