6.4 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 (>, <, ≥, ≤).

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left is either smaller 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 dashed or solid line, then shade the appropriate region based on the inequality.

Front

When do you use a solid line in graphing linear inequalities?

Back

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

Front

When do you use a dashed line in graphing linear inequalities?

Back

A dashed line is used when the inequality is '>' or '<', indicating that points on the line are not 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 (x, y) that satisfy the inequality, represented graphically by the shaded region.

Front

How can you determine which side of the line to shade in a linear inequality?

Back

You can determine which side to shade by testing a point not on the line (usually (0,0)) in the inequality. If it satisfies the inequality, shade that side.