How do you solve $4 |0.5 x - 2.5| = 0$ ?

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answer is B.

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Detailed Solution

The given equation is a Linear equation in one variable as it has only one variable that is x.
For finding the value of x first we have to simplify the equation by removing the mould sign.
For removing that sign we can take 0.5 as common. So,

\Rightarrow 4 |0.5 (x - 5)| = 0

\Rightarrow 4 (0.5) |(x - 5)| = 0

\Rightarrow 2.0 |(x - 5)| = 0

Now, diving into both sides of the equation by 2

\Rightarrow \frac{2 |(x - 5)|}{2} = \frac{0}{2}

\Rightarrow |x - 5| = 0

\Rightarrow x = 5

Now, we know that if

|x| = a

then

x = \pm a

in which, ‘a’ must be a positive number or maybe 0. So,

\Rightarrow |x - 5| = \pm 0

Now, From the properties of modulus, we know that the modulus of any number, whether it is positive or negative, always gives a positive form of that number. This is the reason that ‘a’ cannot be negative. So,