The value of x in the given expression can be either -41 or 45. The correct option is B.
<h3>What is Absolute Value?</h3>
An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.
Given the modulus function (1/5)|x - 4| - 3 = 6. Now, there will be two cases of this because the value of x can be either negative, x<0 or it can positive, x>0. Therefore, the given modulus function can be solved as shown below.
(1/5)(x-4) - 3 = 6
(x/5) - (4/5) - 3 = 6
(x - 4 - 15)/5 = 6
x - 4 -15 = 30
x = 30 + 15 + 4
x = 45
(1/5)(-x+4) - 3 = 6
(-x/5) + (4/5) - 3 = 6
(- x + 4 - 15)/5 = 6
- x + 4 -15 = 30
-x = 30 + 15 - 4
-x = 41
x = -41
Hence, the value of x in the given expression can be either -41 or 45.
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