Question

Please help solve (20 points)
Look at the image below for the question thanks

Answer 1

(D) (6 -z) + (z -5)

Explanation:

You want the equivalent of the absolute value expression for the domain z < 5:

|z -6| -|z -5|

Domain

The expression |z -6| is defined as -(z -6) for z < 6.

The expression |z -5| is defined as -(z -5) for z < 5.

The difference of the two expressions for z < 5 is ...

(-(z -6)) -(-(z -5))

= (6 -z) +(z -5) . . . . . . matches choice D

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Additional comment

The absolute value function negates its argument when that argument is negative. For the given domain, z < 5, both arguments are negative, so both are negated.

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