If \(x\) is a non-negative integer and \(|6 - |x + 2|| = 10,\) then find the number of values of \(x\) that satisfy the

[Gmat_mission]

If \(x\) is a non-negative integer and \(|6 - |x + 2|| = 10,\) then find the number of values of \(x\) that satisfy the given absolute value inequality?

a. 0
b. 1
c. 2
d. 3
e. 4

Answer: B

Source: e-GMAT

[deloitte247]

$$\left|6-\right|x+2\left|\right|=10$$
$$6-\left|x+2\right|=\pm10$$
$$If\ 6-\left|x+2\right|=10,\ then\ \left|x+2\right|=-4\ or\ 16$$
Since the absolute value is not negative
$$\ \left|x+2\right|\ne-4\ $$
$$\ So\ for\ \left|x+2\right|=16$$
$$x+2=\pm16$$
$$x+2=16\ \ \ or\ x+2=-16$$
$$x=14\ \ \ or\ x=-18$$
Since x is non-negative, x = 14
$$If\ 6-\left|x+2\right|=10,\ then\ \left|x+2\right|=16$$
Following the results derived from
$$6-\left|x+2\right|=10,\ x=14$$
Only 1 value satisfies the absolute value; hence option B is the correct answer.