Final answer:
The absolute value inequality 13x+151 < 9 has no solution because an absolute value cannot be less than a negative number. Consequently, there is nothing to graph on the number line, which you would indicate by showing no shaded region.
Step-by-step explanation:
Steps to Solve Absolute Value Inequality and Graph on Number Line
To solve the absolute value inequality 13x+151 < 9, follow these steps:
- Isolate the absolute value expression: Subtract 151 from both sides of the inequality to get |13x| < -142, which is not possible as absolute values yield non-negative results.
- Since an absolute value cannot be less than a negative number, this inequality has no solution.
To graph the solution, you would typically plot the range of x values on a number line and shade the region where the inequality holds true. However, since there is no solution to this inequality, you would indicate this on the number line with no shading and possibly an open circle or a cross-out to show that no x-values satisfy the inequality.
It is important to note that the analytical technique for solving these problems is often more accurate than graphical methods because it depends on precise calculations rather than visual approximations.