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 '>' mean in a linear inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

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

For the inequality y > 4x - 10, where do you shade?

Back

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

Front

For the inequality y < 2x + 3, where do you shade?

Back

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