Change slider based on input

How can I trigger the slider to change/slide/update when the input value of the slider field is changed?
The trouble is my client wants a number input and a slider input to change accordingly when one of those is changed.

The script I have so far is:

function changeInputValue( fieldID, val){
	document.getElementById(fieldID).value = isNaN(parseInt(val, 10)) ? 0 : parseInt(val, 10);
}
function changeRangeValue( fieldID, val){
	var sliderVal = isNaN(parseInt(val, 10)) ? 0 : parseInt(val, 10);
	var slider = document.getElementById(fieldID);
	$(slider).attr('value', sliderVal);
	$(slider).on('change', function(){
		$(slider).next().trigger('update');
	});
}

$("#input_10_7").change(function(){
	changeInputValue('input_10_5', this.value);
});
$("#input_10_5").on('change', function(){
	changeRangeValue('input_10_7', this.value);
});

I can see the input field of the slider gets changed, but how to call the function that slides the handle and changes its value?