The sum of the real values of x satisfying x+2=2 x-2 is:

1968 AMC 12 Problem 9

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The sum of the real values of

x

satisfying

\lvert x+2\rvert=2\lvert x-2\rvert

is:

\dfrac13

\dfrac23

6

6\dfrac13

6\dfrac23

Square both sides; both sides are nonnegative

Use the sum of the roots of the resulting quadratic

Squaring gives

(x+2)^2=4(x-2)^2,

3x^2-20x+12=0.

Both roots satisfy the original absolute-value equation, and their sum is

\frac{20}{3}=6\frac23.

Therefore, the correct answer is E.