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The correct answer is the third option: | 6 | is the distance between 0 and 6, and the distance is always positive regardless of direction.  

Step-by-step explanation:

Distance is a physical measurement, which is never negative. Therefore, the absolute value of a number is never negative.

By this definition, if x is a positive number or 0, then its absolute value is x itself. If x is a negative number, then its absolute value is the additive inverse of x.

Since the absolute value is never negative, then the distance will always be positive, regardless of direction. That is why the third option is the correct

| 6 | is the distance between 0 and 6, and the distance is always positive regardless of direction.  

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4