Expressing and Graphing Inequalities on Number Lines
The image displays a question asking to write the set in interval notation and graph the set on a number line given the inequality x ≤ 19/6.
To write the set in interval notation:
1. Solve the inequality for x. In this case, the inequality is already solved, stating x is less than or equal to 19/6.
2. Express the inequality in interval notation. Since x can take on any value less than or equal to 19/6, the interval notation is (-∞, 19/6].
In interval notation, a square bracket [ or ] indicates that the endpoint is included in the interval (this is the case for 19/6), while a parenthesis ( or ) indicates that the endpoint is not included.
For the graph on the number line:
1. Find the point corresponding to 19/6 on the number line.
2. Since x can be any number less than or equal to 19/6, shade the number line to the left of 19/6 towards negative infinity.
3. At the point 19/6, use a closed dot or bracket to indicate that this endpoint is included in the interval.
I hope this helps you understand how to express the solution and graph it. If you need any further assistance, feel free to ask.
