How do I keep two divs on the same line?

I've been working on a dropdown menu similar to Suckerfish. I've got the dropdown side working now, but I have some images I'm trying to put on either side of the links. Right now I'm using a div the size of the image, then setting the background-image property to the image I need (so that it can change using the pseudo :hover class).

Here is the CSS that applies:

ul#menu3 li {
    color: #000000;
    float: left;
    /*I've done a little playing around here, doesn't seem to do anything*/
    position: relative;
    /*margin-bottom:-1px;*/
    
    line-height: 31px;
    width: 10em;
    padding: none;
    font-weight: bold;
    display: block;
    vertical-align: middle;
    background-image: url(../../images/dropdown/button-tile.gif);
}
.imgDivRt {
    width: 20px;
    height: 31px;
    display: inline;
    float: right;
    vertical-align: middle;
    background-image: url(../../images/dropdown/button-right.gif);
}
.imgDivLt {
    width: 20px;
    height: 31px;
    display: inline;
    float: left;
    vertical-align: middle;
    background-image: url(../../images/dropdown/button-left.gif);
}

I was using selectors to save a little on having different classes, but Internet Explorer doesn't seem to support them :(

Here is my HTML that applies:

<li><div class="imgDivLt"></div>Option 1<div class="imgDivRt"></div>
<ul>
    <li><a href="#"><div class="imgDivLt"></div>Sub 1<div class="imgDivRt"></div></a>
        <ul>
            <li><a href="#"><div class="imgDivLt"></div>Sandwich<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sandwich<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sandwich<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sandwich<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sandwich<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sandwich<div class="imgDivRt"></div></a></li>
        </ul>
    </li>
    <li><a href="#"><div class="imgDivLt"></div>Sub 2<div class="imgDivRt"></div></a> 
    <ul>
            <li><a href="#"><div class="imgDivLt"></div>Sub 1<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sub 2<div class="imgDivRt"></div></a> </li>
            <li><a href="#"><div class="imgDivLt"></div>Sub 3<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sub 4<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sub 5<div class="imgDivRt"></div></a></li>
            <li><a href="#"><div class="imgDivLt"></div>Sub 6<div class="imgDivRt"></div></a></li>
        </ul>
    </li>
    <li><a href="#"><div class="imgDivLt"></div>Sub 3<div class="imgDivRt"></div></a></li>
    <li><a href="#"><div class="imgDivLt"></div>Sub 4<div class="imgDivRt"></div></a></li>
    <li><a href="#"><div class="imgDivLt"></div>Sub 5<div class="imgDivRt"></div></a></li>
    <li><a href="#"><div class="imgDivLt"></div>Sub 6<div class="imgDivRt"></div></a></li>
</ul>
</li>
<li><div class="imgDivLt"></div>Option 2<div class="imgDivRt"></div>

I'm not sure if there's a glitch in my code, or if I'm on the wrong track. It works in Firefox, Safari, and Chrome, but not IE or Opera, so I'm not sure if they're making up for stupidity or what. Ideally, the second image floats greedily to the right in the containing block. In the problem browsers, it sits the next line down (at the far right at least).

Solution

You can make two divs inline this way:

display:inline;
float:left;