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How do I successfully query the checked property?

The checked property of a checkbox DOM element will give you the checked state of the element.

Given your existing code, you could therefore do this (EXAMPLE WITH DEMO LINK):

if(document.getElementById('isAgeSelected').checked) {
    $("#txtAge").show();
} else {
    $("#txtAge").hide();
}

However, there's a much prettier way to do this, using toggle:

$('#isAgeSelected').click(function() {
    $("#txtAge").toggle(this.checked);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" id="isAgeSelected"/>
<div id="txtAge" style="display:none">Age is something</div>

How do I successfully query the checked property?

The checked property of a checkbox DOM element will give you the checked state of the element.

Given your existing code, you could therefore do this:

if(document.getElementById('isAgeSelected').checked) {
    $("#txtAge").show();
} else {
    $("#txtAge").hide();
}

However, there's a much prettier way to do this, using toggle:

$('#isAgeSelected').click(function() {
    $("#txtAge").toggle(this.checked);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" id="isAgeSelected"/>
<div id="txtAge" style="display:none">Age is something</div>

How do I successfully query the checked property?

The checked property of a checkbox DOM element will give you the checked state of the element.

Given your existing code, you could therefore do this:

if(document.getElementById('isAgeSelected').checked) {
    $("#txtAge").show();
} else {
    $("#txtAge").hide();
}

However, there's a much prettier way to do this, using toggle:

$('#isAgeSelected').click(function() {
    $("#txtAge").toggle(this.checked);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" id="isAgeSelected"/>
<div id="txtAge" style="display:none">Age is something</div>

How do I successfully query the checked property?

The checked property of a checkbox DOM element will give you the checked state of the element.

Given your existing code, you could therefore do this (EXAMPLE WITH DEMO LINK):

if(document.getElementById('isAgeSelected').checked) {
    $("#txtAge").show();
} else {
    $("#txtAge").hide();
}

However, there's a much prettier way to do this, using toggle:

$('#isAgeSelected').click(function() {
    $("#txtAge").toggle(this.checked);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" id="isAgeSelected"/>
<div id="txtAge" style="display:none">Age is something</div>

How do I successfully query the checked property?

The checked property of a checkbox DOM element will give you the checked state of the element.

Given your existing code, you could therefore do this:

if(document.getElementById('isAgeSelected').checked) {
    $("#txtAge").show();
} else {
    $("#txtAge").hide();
}

However, there's a much prettier way to do this, using toggle:

$('#isAgeSelected').click(function() {
    $("#txtAge").toggle(this.checked);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" id="isAgeSelected"/>
<div id="txtAge" style="display:none">Age is something</div>

The toggle() method was deprecated in jQuery version 1.8, and removed in version 1.9.

How do I successfully query the checked property?

The checked property of a checkbox DOM element will give you the checked state of the element.

Given your existing code, you could therefore do this:

if(document.getElementById('isAgeSelected').checked) {
    $("#txtAge").show();
} else {
    $("#txtAge").hide();
}

However, there's a much prettier way to do this, using toggle:

$('#isAgeSelected').click(function() {
    $("#txtAge").toggle(this.checked);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" id="isAgeSelected"/>
<div id="txtAge" style="display:none">Age is something</div>