Final answer:
The absolute value equation that has -5 and 1 as solutions is |x + 2| = 3. This is calculated using the midpoint between -5 and 1 and considering the distance to either point from the midpoint.
Step-by-step explanation:
The student is asking for an absolute value equation that has solutions of -5 and 1 on the number line. To create an equation that meets this criterion, we look for a value that is equidistant from both -5 and 1 on the number line. The midpoint between -5 and 1 is -2, and the distance from this midpoint to either of the two points is 3. Therefore, the absolute value equation that represents this situation is |x + 2| = 3.
The absolute value equation can be solved by considering both the positive and negative scenarios. For the equation |x + 2| = 3, the solutions are obtained as follows:
- x + 2 = 3, which gives us x = 1
- x + 2 = -3, which gives us x = -5
These are the same values that are given, which shows that the equation |x + 2| = 3 indeed has the solutions we are looking for.