how do absolute values work | Mathematics | Page 1

hello could anyone explain how it can be determined that the absolute value bars on x can be omitted here, and also how |ln(v)-1| became ln(v)-1?

v is a function of x, and c is some real constant. this is from houston math prep: homogeneous first order differential equations part 2: https://youtu.be/Go5hX8UvqiQ (example 3)

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Houston Math Prep

Homogeneous First-Order Differential Equations (Examples)

We work some examples of homogeneous first-order differential equations. We show all of the examples to be worked at the beginning of the video, so you can choose to watch all of the examples, or skip to a particular example that you would like to see. In these examples, we focus on: testing for a homogeneous differential equation, making the ...

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