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1. Using MS Word 2003 or Earlier Versions
If you have Microsoft Office 2003, or an earlier version installed on your computer, just download and install the Microsoft Compatibility Pack and you'll soon be able to open a .docx file with your current installation of Word. This is a free download from Microsoft to help transition the move to the newer file format.
2. Use the Cloud
Using Google Docs is one of the quickest and easiest ways of opening a .docx file. This method does not require you to install any software on your computer, and you can just upload your .docx file to Google Docs and use it as normal. Alternatively, you can try the new Microsoft Office Web Apps. These are Microsoft's version of Google Docs and they will read your .docx file with ease when you upload it to your Windows Live account.
3. Try OpenOffice
Open Office is a free office suite that is a lot like the original MS Office. It includes a word processor that will open a variety of file formats, including .docx files. One benefit of OpenOffice is that it is also available in a portable form, which you can download onto your USB flash drive to make the process faster and easier.
4. Use Internet Explorer
This technique will let you read .docx files without using the internet or downloading any additional software. The .docx files are simply zip files renamed, and if you uncompress them like any other zip file, you can then open them with Internet Explorer. Just rename your file extension from .docx to .zip, extract its contents using WinZip, (or any other zip program you use), go into the “Word” folder, and open document.xml in Internet Explorer. Internet Explorer will display the file contents just as you see it in Word.

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5. Use Online .docx Converters
There are plenty of online tools available that will easily solve the problem of how to open a docx file by converting it to a .doc or some other format. All you need to do is navigate to the website that offers this service, upload your .docx file, and wait as it is converted to the format you choose. The free online .docx file converters include:
A. Zamzar
B. Investintech
C. Docx converter