I found this shelf already attached to supports and I'd like to put it up on the back of this cedar closet. The cedar closet is built out of a frame of 2"x4"s, but the width between the 2x4s doesn't line up with the shelf supports. See below:
I have more 2x4s and other scrap wood. Should I cut out and screw in two horizontal 2x4s on the inside gap in between the existing vertical 2x4s, to fill the gaps and screw the shelf into the new horizontal 2x4s? I may line up the shelf support on one of the existing 2x4s, then just fill in the gap for the other shelf support using one or two horizontal 2x4s to make a sturdy spot the shelf can screw into. Here's a sketch of what I'm talking about:
Is there a better way to go about this? Will my horizontal 2x4 additionals hold up the shelf sufficiently?