Graphing Inequalities

Front

What is an inequality?

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 does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph the inequality b ≤ –2?

Back

To graph b ≤ –2, draw a horizontal line at y = -2, use a solid line to indicate that -2 is included, and shade the area below the line.

Front

What does the inequality x < 6 indicate about the value of x?

Back

The inequality x < 6 indicates that x can take any value less than 6, but not equal to 6.

Front

How do you represent the inequality k < 3 on a graph?

Back

To represent k < 3, draw a horizontal line at y = 3 with a dashed line to indicate that 3 is not included, and shade the area below the line.

Front

What is the difference between '>' and '≥'?

Back

The symbol '>' means 'greater than' and does not include the value, while '≥' means 'greater than or equal to' and includes the value.

Front

How do you determine which graph represents the inequality p < 2?

Back

To determine the correct graph for p < 2, look for a horizontal line at y = 2 with a dashed line and shading below the line.

Front

What does the graph of an inequality indicate?

Back

The graph of an inequality indicates all the possible solutions that satisfy the inequality.

Front

What is the significance of using a solid line versus a dashed line in graphing inequalities?

Back

A solid line indicates that the boundary value is included in the solution (≤ or ≥), while a dashed line indicates that it is not included (< or >).

Front

How can you check if a point is a solution to an inequality?

Back

To check if a point is a solution to an inequality, substitute the point's coordinates into the inequality and see if the statement is true.