如何从PHP调用Bootstrap Modal？

Quick question. How do I call a Bootstrap Modal from PHP? I have a form and when some error happen I want to show an alert modal to the user. I've tried many solutions from other topics but neither has worked.

Here's what I've tried last:

echo '<script type="text/javascript">';
echo '$(\'#alertDuplicate\').modal(\'show\')';
echo '</script>';

and here's the modal:

<!-- Modal Alert Duplicate -->
    <div class="modal fade" id="alertDuplicate">
        <div class="modal-dialog" role="document">
            <div class="modal-content">
                <div class="modal-header">
                    <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>
                    <h4 class="modal-title">Erro</h4>
                </div>
                <div class="modal-body">
                    <p>Essa função já existe!</p>
                </div>
                <div class="modal-footer">
                    <button type="button" class="btn btn-default" data-dismiss="modal">Fechar</button>
                </div>
            </div><!-- /.modal-content -->
        </div><!-- /.modal-dialog -->
    </div><!-- /.modal -->

Try putting that into a document ready function like this:

echo '<script type="text/javascript">';
echo '$(document).ready(function() {';
echo '$("#alertDuplicate").modal("show");';
echo '});';
echo '</script>';

You can use the example below or you can use ajax to call and return the response from your php script.

echo <<<EOT
<script type="text/javascript">
$(document).ready(function() {
    $('#alertDuplicate').modal('show');
});
</script>
EOT;

AJAX EXAMPLE

With ajax you can use something like this:

<script type="text/javascript">
$(document).ready(function () {
    $("input#submit").click(function(){
        $.ajax({
            type: "POST",
            url: "YOUR_PHP_FILE.php",
            data: $('form.FORM_NAME').serialize(),
            success: function(msg){
                $("#alertDuplicate").modal('hide');
            },
            error: function(){
                $("#alertDuplicate").modal('show');
            }
        });
    });
});
</script>

(You have to change the words "FORM_NAME" and "YOUR_PHP_FILE" with your needs)