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This problem is probably related to the text format used when the page containing the image is rendered.

If the text format used is "Filtered HTML", you should try to change the format for the node to "Full HTML".  If this change makes the missing images re-appear, the problem is the text format.

If only trusted users are allowed to insert images in nodes, you can fix the problem by changing the default text format from "Filtered HTML" to "Full HTML".  However, it is not recommended to allow untrusted users use this text format, as it allows XSS attacks.

For a secure configuration where untrusted users can insert images, you need to use a better filter module that the default "Filtered HTML".  You can do this by installing the WYSIWYG Filter module as is decribed here.