Question 1207367
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For (a), the answer is  {{{abs(pi-4)}}} + 1 = {{{(4-pi)}}} + 1 = {{{5-pi}}}.


For (b), |x-5| given that x >= 5  is x-5   (by the definition of the absolute value)


For (c), |t-5| given that t < 5  is -(t-5),  or  5-t.   (by the definition of the absolute value)
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Solved, answered and explained, in full.


As a prerequisite, you must know/read/understand the definition of the absolute value.



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<U>Comment from student</U> : Good reply. For part (a), the book's answer is -pi + 5. Does it matter if I write it as you did: 5 - pi?



<U>My response</U> : &nbsp;&nbsp;-pi+5 is the same &nbsp;(is equal to) &nbsp;5-pi.
It is as clear as a sunny day, &nbsp;and any school student can confirm it . . .