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 such as <, >, ≤, or ≥.

Front

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

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How do you graph a linear inequality with '<' or '>'?

Back

You graph it using a dashed line to indicate that points on the line are not included in the solution.

Front

How do you graph a linear inequality with '≤' or '≥'?

Back

You graph it using a solid line to indicate that points on the line are included in the solution.

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

How do you determine which side of the line to shade when graphing a linear inequality?

Back

You can test a point not on the line (like (0,0)) to see if it satisfies the inequality; if it does, shade that side.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., y = mx + b), while a linear inequality shows a range of values (e.g., y < mx + b).