Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '<' represent?

Back

The symbol '<' represents 'less than'.

Front

How do you graph a linear inequality with a solid line?

Back

You graph a linear inequality with a solid line when the inequality includes '≤' or '≥', indicating that points on the line are included in the solution.

Front

How do you graph a linear inequality with a dashed line?

Back

You graph a linear inequality with a dashed line when the inequality includes '<' or '>', indicating that points on the line are not included in the solution.

Front

Back

You shade above the line because the inequality is 'greater than'.

Front

Back

You shade below the line because the inequality is 'less than or equal to'.

Front

What is the difference between 'greater than' and 'greater than or equal to'?

Back

'Greater than' (>) means the value is not included, while 'greater than or equal to' (≥) means the value is included.

Front

What does it mean to 'shade' in the context of graphing inequalities?

Back

Shading indicates the region of the graph that satisfies the inequality.

Front

How do you determine which side 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 solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.