Question 1121927: How do you write an absolute value equation that has the solutions x=−10
and x=−5? Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
Use the idea that
means b is the distance between x and a.
In your example, the values x=-10 and x=-5 are each a distance of 2.5 from x = -7.5. So the absolute value equation you want is the one that says the distance between x and -7.5 is 2.5.
Use the pattern to insert the numbers in your example.
If you don't quite understand yet, here is another example.
Suppose we want the two solutions to be -10 and 34.
The point midway between -10 and 34 is ((-10+34)/2) = 12; the distance between 12 and either -10 or 34 is 22.
So the absolute value equation has to say that the distance between x and 12 is 22. Plugging those numbers into the pattern gives us the answer:
