SOLUTION: Write an absolute value equation that has the solutions x=−6 and x=10.

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Question 1124599: Write an absolute value equation that has the solutions x=−6 and x=10.


Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
equation that has the solutions x%5B1%5D=-6 and x%5B2%5D=10 is
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
f%28x%29=%28x-%28-6%29%29%28x-10%29
f%28x%29=%28x%2B6%29%28x-10%29
f%28x%29=x%5E2-10x%2B6x-60
f%28x%29=x%5E2-4x-60
an absolute value equation is:
f%28x%29=abs%28x%5E2-4x-60%29


+graph%28+600%2C+600%2C+-10%2C+20%2C+-10%2C+80%2C+abs%28x%5E2-4x-60%29%29+


Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
The simplest possible equation is


    |x - 2| = 8.


Notice that the number 2 is exactly half-way between the points " -6 "  and  " 10 " on the number line: 
it is a midpoint, or a bisector of the segment  [-6,10].



The number " 8 " in the right side of the equation is the distance from midpoint " 2 " to endpoints.

Notice that 8 is exactly half of the length of the segment  [-6,10], which (the length) is 16 units.



The equation says:  the distance from the point  " x "  to the  point " 2 "  is equal to 8.


This equation has exactly two solutions  x= -6  and  x= 10, as it is required.

If next time you will get similar problem, do the same steps to get the answer.