How smart are you? I was bored

One word WORK

1 If 1/2x +1/2(1/2x + 1/2(1/2x +1/2(1/2x + ... = y, then x = ?
2 -5x = -45, What =X?
3 A man was to be sentenced, and the judge told him, "You may make a statement. If it is true, I'll sentence you to four years in prison. If it is false, I'll sentence you to six years in prison." After the man made his statement, the judge decided to let him go free. What did the man say?
4 When is it bad luck to meet a white cat?
5 What stinks when living and smells good when dead?
6 Food can help me survive, but water will kill me. What am I?
7 What has a mouth but can't chew?
8 Why wasn't John able to take a photo of his mother with curlers?