SOLUTION: If x is twice as far from -9 as it is from 3,what are the possible values of x?

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Question 1148045: If x is twice as far from -9 as it is from 3,what are the possible values of x?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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            It can be solved algebraically,  but a geometric solution is more impressive -- so,  I will show you it . . .


We should consider  3  cases 


a)  On the number line, "x" is to the left from -9.

        Then it is clear that THERE IS NO solution in this case.

         (It is OBVIOUS, so I will not try to prove it).



b)  On the number line, "x" is between  -9 and 3.

        Then the distance from -9 to 3 is 12 units, and we should divide it in proportion 2:1, counting from left to right.


        Obviously, the point x= -1 divide the segment [-12,3] in this proportion.

        So, x= -1 is the solution in this case.



c)  On the number line, "x" is to the right from 3.


        Again, recall that the distance from -9 to 3 is 12 units;

        so, we need move 12 units to the right from 3; then we get x= 3+12 = 15.

        Thus x= 15 is the solution in this case.


ANSWER.  The problem has two solutions:  x= -1  and  x= 15.

Solved and completed.