**Core Concept**
Sclerosing osteitis, also known as Garre's sclerosing osteitis, is a benign bone lesion characterized by a periosteal reaction and cortical thickening, often accompanied by an ill-defined border on radiographic images. This lesion is a type of periosteal reaction that can be seen in various conditions, including infection, trauma, and neoplasms.

**Why the Correct Answer is Right**
Sclerosing osteitis displays an ill-defined border on radiographs due to the periosteal reaction and cortical thickening associated with the lesion. The periosteum, a layer of connective tissue surrounding the bone, reacts to underlying bone damage by proliferating and forming new bone tissue. This process can lead to an irregular, ill-defined border on radiographs, distinguishing sclerosing osteitis from other bone lesions with well-defined borders. The characteristic periosteal reaction and cortical thickening in sclerosing osteitis make it a key differentiator from other lesions.

**Why Each Wrong Option is Incorrect**
**Option A:** Periapical cysts typically have well-defined borders and are characterized by a radiolucent lesion in the periapical region of a tooth. They do not display the periosteal reaction and cortical thickening seen in sclerosing osteitis.
**Option C:** Soft tissue capsules surrounding bone lesions can appear as well-defined borders on radiographs, but they do not exhibit the characteristic periosteal reaction and cortical thickening of sclerosing osteitis.
**Option D:** Multiple myeloma lesions often have well-defined borders and can appear as lytic lesions on radiographs, but they do not typically display the periosteal reaction and cortical thickening associated with sclerosing osteitis.

**Clinical Pearl / High-Yield Fact**
When evaluating bone lesions on radiographs, it's essential to distinguish between lesions with well-defined borders, such as periapical cysts, and those with ill-defined borders, like sclerosing osteitis. The presence of a periosteal reaction and cortical thickening can help differentiate sclerosing osteitis from other bone lesions.

**✓ Correct Answer: B. Sclerosing osteitis**