Complex sentence: By the 1950s, it appeared that absolute poverty was a minor problem pockets did remain, for example among the elderly, but it was believed that increased welfare benefits would soon eradicate this lingering poverty.
Split into simpler sentences: By the 1950s, it appeared that poverty was a minor problem. "Pockets" remained--for example, among the elderly--but it was believed that increased welfare benefits would soon eradicate this lingering poverty.