Graphing 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 '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value can be greater than or equal to a certain number.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value must be less than a certain number.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then shade the region that represents the solution set.

Front

What does it mean if a graph has a solid line?

Back

A solid line indicates that the points on the line are included in the solution set (used for inequalities with ≤ or ≥).

Front

What does it mean if a graph has a dashed line?

Back

A dashed line indicates that the points on the line are not included in the solution set (used for inequalities with < or >).

Front

If the inequality is x < -3, which direction do you shade on the graph?

Back

You shade to the left of -3, indicating all values less than -3 are included in the solution set.

Front

If the inequality is x ≥ -1, which direction do you shade on the graph?

Back

You shade to the right of -1, indicating all values greater than or equal to -1 are included in the solution set.

Front

What is the solution set for the inequality x < 2?

Back

The solution set includes all values less than 2.

Front

What is the solution set for the inequality x ≥ 1?

Back

The solution set includes all values greater than or equal to 1.