Graphing Inequalities 2.6

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is any number less than 5.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is any number greater than or equal to 2.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is any number less than or equal to 4.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region based on the inequality.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

How can you determine if a point is part of the solution set of an inequality?

Back

To determine if a point is part of the solution set, substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

What is a boundary line in the context of inequalities?

Back

A boundary line is the line that represents the equation of the inequality. It divides the graph into two regions: one that satisfies the inequality and one that does not.