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, or not equal to the other.

Front

What does the symbol '≤' represent?

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 represent on a number line?

Back

The inequality x < 6 represents all numbers less than 6, graphed with an open circle at 6 and shading to the left.

Front

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

Back

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

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 an open circle at 3 and shade the area below the line.

Front

What does the number line graph with an arrow pointing to the right from -5 represent?

Back

The number line graph with an arrow pointing to the right from -5 represents the inequality x ≥ -5, indicating all numbers greater than or equal to -5.

Front

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

Back

A solid line indicates that the boundary value is included in the solution set, meaning the inequality is '≤' or '≥'.

Front

What does an open circle on a number line indicate?

Back

An open circle indicates that the endpoint is not included in the solution set, meaning the inequality is '<' or '>'.

Front

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

Back

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