The absolute value equation with the solutions x = -6 and x = 10 is:
|x - 2| = 8
How to find an absolute value equation with the two given solutions?
A general absolute value equation is:
|x - b| = a
Such that can be decomposed into two simple equations:
x - b = a
x - b = -a
Now, we know that the two solutions (one for each of these equations) are x = -6 and x = 10.
10 - b = a
-6 - b = -a
(the negative solution is the one we use for the equation with the negative value of a).
Now, to solve the system of equations, we can replace "a" of the first equation into the second one, so we have:
-6 - b = -(10 - b)
-6 - b = -10 + b
-6 + 10 = 2b
4/2 = b = 2
Now, the value of a is:
10 - b = a
10 - 2 = a
8 = a
The absolute value equation with the solutions x = -6 and x = 10 is:
|x - 2| = 8
If you want to learn more about absolute value equations:
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