Answer:
First Option: Workers were at risk of having their jobs replaced by machines.
Step-by-step explanation:
In this passage from Modern History Sourcebook: Leeds Woollen Workers Petition, 1786, the main concern of the petition is that new machines are taking away worker's jobs and businesses. Even if they somehow learn new machines and adopt new businesses, they are not sure for if that business and machine too is taken away by yet another machine.
Second and third options are incorrect because there is no mention in the passage about dangers to worker's health, being deprived of education and families having to take extra jobs.