If you have configured your view to display all events that has start date >= x and end date <= x then what you have done show do the job.
In order to make it easy for others to help you, I recommend that you give description of your content types date fields, update your question with export code of your view so that others look and spot mistakes if any.
In the meantime, I have created a content type called event, and give it one field called i.e. date (I have configured the date field to collect both start date and end date - only year/month/day). I then setup a view and setup two exposed filters on start_date and end_date of this content type with operators as greator than or equal to and less than or equal to, and they seem to work without any problem. Follow is the export code of my view
$view = new view();
$view->name = 'events';
$view->description = '';
$view->tag = 'default';
$view->base_table = 'node';
$view->human_name = 'Events';
$view->core = 7;
$view->api_version = '3.0';
$view->disabled = FALSE; /* Edit this to true to make a default view disabled initially */
/* Display: Master */
$handler = $view->new_display('default', 'Master', 'default');
$handler->display->display_options['title'] = 'Events';
$handler->display->display_options['use_more_always'] = FALSE;
$handler->display->display_options['access']['type'] = 'perm';
$handler->display->display_options['cache']['type'] = 'none';
$handler->display->display_options['query']['type'] = 'views_query';
$handler->display->display_options['exposed_form']['type'] = 'basic';
$handler->display->display_options['exposed_form']['options']['reset_button'] = TRUE;
$handler->display->display_options['pager']['type'] = 'full';
$handler->display->display_options['pager']['options']['items_per_page'] = '10';
$handler->display->display_options['style_plugin'] = 'default';
$handler->display->display_options['row_plugin'] = 'fields';
/* Field: Content: Title */
$handler->display->display_options['fields']['title']['id'] = 'title';
$handler->display->display_options['fields']['title']['table'] = 'node';
$handler->display->display_options['fields']['title']['field'] = 'title';
$handler->display->display_options['fields']['title']['label'] = '';
$handler->display->display_options['fields']['title']['alter']['word_boundary'] = FALSE;
$handler->display->display_options['fields']['title']['alter']['ellipsis'] = FALSE;
/* Field: Content: date */
$handler->display->display_options['fields']['field_date']['id'] = 'field_date';
$handler->display->display_options['fields']['field_date']['table'] = 'field_data_field_date';
$handler->display->display_options['fields']['field_date']['field'] = 'field_date';
$handler->display->display_options['fields']['field_date']['settings'] = array(
'format_type' => 'long',
'fromto' => 'both',
'multiple_number' => '',
'multiple_from' => '',
'multiple_to' => '',
);
/* Sort criterion: Content: Post date */
$handler->display->display_options['sorts']['created']['id'] = 'created';
$handler->display->display_options['sorts']['created']['table'] = 'node';
$handler->display->display_options['sorts']['created']['field'] = 'created';
$handler->display->display_options['sorts']['created']['order'] = 'DESC';
/* Filter criterion: Content: Published */
$handler->display->display_options['filters']['status']['id'] = 'status';
$handler->display->display_options['filters']['status']['table'] = 'node';
$handler->display->display_options['filters']['status']['field'] = 'status';
$handler->display->display_options['filters']['status']['value'] = 1;
$handler->display->display_options['filters']['status']['group'] = 1;
$handler->display->display_options['filters']['status']['expose']['operator'] = FALSE;
/* Filter criterion: Content: Type */
$handler->display->display_options['filters']['type']['id'] = 'type';
$handler->display->display_options['filters']['type']['table'] = 'node';
$handler->display->display_options['filters']['type']['field'] = 'type';
$handler->display->display_options['filters']['type']['value'] = array(
'eventsbydate' => 'eventsbydate',
);
/* Filter criterion: Content: date - start date (field_date) */
$handler->display->display_options['filters']['field_date_value']['id'] = 'field_date_value';
$handler->display->display_options['filters']['field_date_value']['table'] = 'field_data_field_date';
$handler->display->display_options['filters']['field_date_value']['field'] = 'field_date_value';
$handler->display->display_options['filters']['field_date_value']['operator'] = '>=';
$handler->display->display_options['filters']['field_date_value']['exposed'] = TRUE;
$handler->display->display_options['filters']['field_date_value']['expose']['operator_id'] = 'field_date_value_op';
$handler->display->display_options['filters']['field_date_value']['expose']['label'] = 'date (field_date)';
$handler->display->display_options['filters']['field_date_value']['expose']['operator'] = 'field_date_value_op';
$handler->display->display_options['filters']['field_date_value']['expose']['identifier'] = 'field_date_value';
$handler->display->display_options['filters']['field_date_value']['expose']['remember_roles'] = array(
2 => '2',
1 => 0,
3 => 0,
);
$handler->display->display_options['filters']['field_date_value']['group_info']['label'] = 'date (field_date)';
$handler->display->display_options['filters']['field_date_value']['group_info']['identifier'] = 'field_date_value';
$handler->display->display_options['filters']['field_date_value']['group_info']['remember'] = FALSE;
$handler->display->display_options['filters']['field_date_value']['group_info']['group_items'] = array(
1 => array(),
2 => array(),
3 => array(),
);
/* Filter criterion: Content: date - end date (field_date:value2) */
$handler->display->display_options['filters']['field_date_value2']['id'] = 'field_date_value2';
$handler->display->display_options['filters']['field_date_value2']['table'] = 'field_data_field_date';
$handler->display->display_options['filters']['field_date_value2']['field'] = 'field_date_value2';
$handler->display->display_options['filters']['field_date_value2']['operator'] = '<=';
$handler->display->display_options['filters']['field_date_value2']['exposed'] = TRUE;
$handler->display->display_options['filters']['field_date_value2']['expose']['operator_id'] = 'field_date_value2_op';
$handler->display->display_options['filters']['field_date_value2']['expose']['label'] = 'date - end date (field_date:value2)';
$handler->display->display_options['filters']['field_date_value2']['expose']['operator'] = 'field_date_value2_op';
$handler->display->display_options['filters']['field_date_value2']['expose']['identifier'] = 'field_date_value2';
$handler->display->display_options['filters']['field_date_value2']['expose']['remember_roles'] = array(
2 => '2',
1 => 0,
3 => 0,
);
/* Display: Page */
$handler = $view->new_display('page', 'Page', 'page');
$handler->display->display_options['path'] = 'events';
screenshot of the configuration page is as follow

If the above approach does not help you then have a look at this useful module https://www.drupal.org/project/views_between_dates_filter