Set admin body to ltr on a rtl installation

Important: You shouldn’t modify core files, because you might loose
all your edits in the next core upgrade.

You should instead enqueue your own stylesheet with your custom CSS modifications through the admin_enqueue_scripts hook or use a hook like admin_head to implement your customization.

Here’s an example:

/**
 * Force #wpbody to the 'ltr' direction:
 */

add_action( 'admin_head', function(){
 echo '<style> #wpbody { direction:ltr !important; } </style>
';
});

These kind of modifications are suitable as a plugin. Create a file like /wp-content/plugins/wpse-admin-ltr/wpse-admin-ltr.php, with your code for modifications:

<?php
 /**
  * Plugin Name: WPSE - Force ltr admin layout
  * Author:      Yair Levy
  * Description: Force #wpbody to the 'ltr' direction:
  * Version:     0.0.1
  */

 // ----------- your custom code here -------------

Check the Codex for more detailed instructions on how to write a plugin.

Just remember to use the WP_DEBUG on your dev site.

I hope this helps.