SOLUTION: How do you write an absolute value equation that has the solutions x=−10 and x=−5?

Algebra.Com
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): You can put this solution on YOUR website!


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:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
A TWIN problem was solved at the link

https://www.algebra.com/algebra/homework/absolute-value/absolute-value.faq.question.1121926.html

https://www.algebra.com/algebra/homework/absolute-value/absolute-value.faq.question.1121926.html


Use it as your sample.



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