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Google might not index your website in Google if your website is not mobile friendly.
A responsive webste is the cheapest solution to make a website mobile friendly. This is an "extensible website", this means it is adapted to the width of the screen.
Even if this leads to some graphic changes of your website, in order to make your website responsive you need to add the Viewport tag in the head of your page.
<meta name="viewport" content="width=device-width, initial-scale=1.0, shrink-to-fit=no">
This tag indicates to the browsner not to "dezoom" your page and thus keep texts in a readable size.
The most powerful solution from an ergonomic point of view but the solution the more expensive is to create a mobile version of the page. The mobile version involves creating and maintaining two different versions of a page.
In order to indicate to the browser that there is a mobile version, you can use the Link tab:
<link rel="alternate" media="only screen and (max-width: 640px)" href="http://m.website.com/">
Here is the article from Google about how to make your website Mobile friendly.