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 (>, <, ≥, ≤) instead of an equal sign.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the expression on the left is greater than or equal to the expression on the right.

Front

How do you write a linear inequality for a situation involving money?

Back

Identify the variables, set up an inequality based on the conditions given, and express it in standard form.

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

When do you use a solid line when graphing a linear inequality?

Back

A solid line is used when the inequality includes '≥' or '≤', indicating that points on the line are included in the solution.

Front

What does the symbol '<' mean in a linear inequality?

Back

The symbol '<' means that the expression on the left is less than the expression on the right.

Front

How do 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.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points that satisfy the inequality, often represented as a shaded region on a graph.

Front

What does it mean if a system of linear inequalities has 'No Solution'?

Back

'No Solution' means that there is no set of values that satisfies all inequalities in the system simultaneously.