Graphing Inequalities 2.6

Front

What is an inequality in mathematics?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What are the symbols used to represent inequalities?

Back

The symbols used to represent inequalities are: > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

Front

How do you graph a linear inequality in two variables?

Back

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

Front

What does it mean to shade above the line in a graph of an inequality?

Back

Shading above the line indicates that the solutions to the inequality are all the points where the y-value is greater than the value of the line at that x-value.

Front

What does it mean to shade below the line in a graph of an inequality?

Back

Shading below the line indicates that the solutions to the inequality are all the points where the y-value is less than the value of the line at that x-value.

Front

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

Back

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

Front

How can you determine which side of the line to shade when graphing an inequality?

Back

You can determine which side to shade by selecting a test point not on the line (commonly (0,0) if it is not on the line) and substituting it into the inequality. If the inequality holds true, shade that side; if not, shade the opposite side.

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities, typically using 'and' or 'or' to connect them.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, solve each inequality separately and then combine the solutions. For 'and', the solution is the intersection; for 'or', it is the union.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line separates the graph into two regions, indicating where the solutions to the inequality lie.