The sentences are good as is, but not very casual. If you want more casual sentences, (I don't mean better, just more like the way people might talk) here are some ideas: •He keeps quiet so he won't be a distraction/won't distract anybody. •He kept the speech vague; he didn't commit to either side. •I wrote down her name so I wouldn't forget it. •I came to see you not to complain, but to apologize. THIS ONE IS ALREADY FINE • The model was designed so that the value of x could be calculated. • The advertisement is printed in such a way that you can see two very different pictures depending on how you look at it. • Our business is managed so as to minimize its environmental impact

Could be: "He keeps schtum so not to cause a distraction" "He sat on the fence by keeping his speech vague" "I jotted her name down so I'd remember it" "I didn't come here to complain, but to say sorry" "The model was designed so you can work out x" "The advert is made so you can see two different pictures depending on how you look at it" "We try to make our business as good for the environment as we can".

re: "He stays silent in order not to be a distraction." This is technically fine, but not a smooth casual tone. Consider this more casual alternative: "He's staying silent so he won't distract us."