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.

Tags

CCSS.8.EE.C.8B

Front

How do you represent a word problem as a system of inequalities?

Back

Identify the variables, determine the constraints (limits) and objectives, and translate them into inequalities based on the relationships described in the problem.

Front

What does the inequality x + y ≤ 6 represent in a word problem?

Back

It indicates that the total of two quantities, x and y, cannot exceed 6, often representing a limit on resources or time.

Front

What does the inequality 32x + 20y ≥ 150 represent in a word problem?

Back

It indicates that the total output from two activities (x and y) must meet or exceed a certain requirement, in this case, at least 150 cookies.

Front

What is the significance of the '≥' symbol in inequalities?

Back

The '≥' symbol means 'greater than or equal to,' indicating that the value can be either greater than or exactly equal to the number.

Tags

CCSS.6.EE.B.8

Front

What is the significance of the '<' symbol in inequalities?

Back

The '<' symbol means 'less than,' indicating that the value must be strictly less than the number.

Tags

CCSS.6.EE.B.8

Front

How do you determine the feasible region for a system of inequalities?

Back

Graph each inequality on the same coordinate plane and identify the overlapping region that satisfies all inequalities.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a point is in the feasible region of a system of inequalities?

Back

It means that the point satisfies all inequalities in the system, making it a potential solution to the problem.

Tags

CCSS.HSA.REI.D.12

Front

What is the first step in solving a word problem involving systems of inequalities?

Back

Identify the variables that represent the quantities in the problem.

Front

How can you check if a solution satisfies a system of inequalities?

Back

Substitute the solution values into each inequality and verify that all inequalities hold true.