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 (e.g., <, >, ≤, ≥).

Front

What does the symbol '≤' mean 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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then shade the region that satisfies the inequality.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is typically written as Ax + By ≤ C or Ax + By ≥ C, where A, B, and C are constants.

Front

What does it mean if a solution is in the shaded region of a graph?

Back

If a solution is in the shaded region of a graph, it means that the values of x and y in that region satisfy the inequality.

Front

What is the difference between 'y > mx + b' and 'y ≥ mx + b'?

Back

'y > mx + b' represents a dashed line and the area above it, while 'y ≥ mx + b' includes the line itself and the area above it.

Front

How do you write a linear inequality from a word problem?

Back

Identify the variables, determine the relationship between them, and express the condition using an inequality symbol.

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 inequalities in the system.

Front

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

Back

The boundary line indicates the limit of the solution set; points on the line may or may not be included based on the inequality symbol.

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.