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Buy 2 adhesive wall strips and 2 clothespins from a craft store. Stick the wall adhesive strips to the clothespins. Press the clothespins onto the wall. Attach the tapestry to the clothespins.
Medium to large-sized clothespins work best for hanging tapestries. Choose adhesive wall strips that are approximately the same size as your clothespins. If no wall strips match the exact size of your clothespins, go a size larger—you can always trim them as needed later. Attach the clothespin to one side of the wall adhesive strip. Press the strip and clothespin together tightly to keep either from detaching as you hang the tapestry.  If you wall adhesive strips are not double-sided, a wood glue to glue the clothespins to the strips. If the wall adhesive strips are too large, cut them to size with scissors before gluing. Measure the length of your tapestry and attach the clothespins so they can hold up both ends of the tapestry. Follow the wall adhesive strip directions carefully so the clothespins stay secure on the wall. If your tapestry is large, purchase and attach 3 clothespins to the wall—one on both ends and one in the middle. When you've clamped the tapestry down with the clothespins, stand back and inspect it. If your tapestry appears to droop in the middle, you may not have spread your clothespins out enough. Re-apply the clothespins to the wall or add a third clothespin in the middle to prevent drooping.  If you need to re-apply the clothespins, you may need to replace the wall adhesive strips. Some lose their sticking properties each time they are removed to the wall. The clothespin method is best for thin tapestries--thicker ones might not stay as tightly clamped.