Problem Solving: Systems of Linear 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 (>, <, ≥, ≤).

Front

What does the symbol '≥' mean in inequalities?

Back

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

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

How do you represent a situation with two variables using inequalities?

Back

You can represent a situation with two variables using inequalities by defining the variables and writing inequalities based on the conditions given.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a shaded region on one side of a boundary line, which represents all the solutions to the inequality.

Front

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

Back

The solution set of a system of linear inequalities represents all the points that satisfy all the inequalities in the system.

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line in a linear inequality separates the solution set from the non-solution set. It is solid for '≥' or '≤' and dashed for '>' or '<'.

Front

How can you express a real-world problem as a system of linear inequalities?

Back

Identify the variables, determine the constraints, and write inequalities that represent those constraints based on the problem's conditions.

Front

What is the maximum number of shots Cole can take in the basketball challenge?

Back

Cole can take less than 10 shots, represented by the inequality x + y < 10.