Write an absolute value equation that has the solutions x=2.5, x=-3.5

You can develop an equation by thinking about how absolute value is used for distances between two numbers.

The number that is between - 3.5 and 2.5 is the average number between the two:

avg = (-3.5 + 2.5) / 2 = - 0.5

The distance between the middle of - 0.5 and 2.5 is the same as the distance between the middle of - 0.5 and - 3.5.

Distance = | 2.5 - (-0.5) | OR | - 3.5 - (-0.5) |

= | 2.5 + 0.5 | OR | - 3.5 + 0.5 |

and that distance is equal to 3.

So a possible equation is

|x + 0.5| = 3

and this has solutions of x = - 3.5 and x = 2.5 as demonstrated above