Review Linear Inequalities and 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 (such as <, >, ≤, or ≥).

Front

How do you write a linear inequality in standard form?

Back

A linear inequality in standard form is typically written as Ax + By ≤ C, where A, B, and C are constants, and x and y are variables.

Front

What does the symbol '≤' represent in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a region on a coordinate plane, often bounded by a line, where all points in the region satisfy the inequality.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means 'greater than' and does not include the boundary, while '≥' means 'greater than or equal to' and includes the boundary.

Front

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

Back

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

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality separately, shading the appropriate region, and then identify the overlapping shaded area as the solution.

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. It is solid for '≤' or '≥' and dashed for '<' or '>'.

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on a graph where all constraints of a system of inequalities are satisfied.