Two things to keep in mind when you're deciding whether to use formal or informal english are the
a. occasion and the audience.
b. opinion and the occasion.
c. reader and the audience.
d. reader and the location.

read this passage from the crisis. what rationale is paine using for going to war with great britain? my own line of reasoning is to myself as straight and clear as a ray of light. not all the treasures of the world, so far as i believe, could have induced me to support an offensive war, for i think it murder; but if a thief breaks into my house, burns and destroys my property, and kills or threatens to kill me, or those that are in it, and to "bind me in all cases whatsoever" to his absolute will, am i to suffer it? what signifies it to me, whether he who does it is a king or a common man; my countryman or not my countryman; whether it be done by an individual villain, or an army of them? if we reason to the root of things we shall find no difference; neither can any just cause be assigned why we should punish in the one case and pardon in the other.

it is waged war against an army of countrymen

it would lead to independence from britain

it would be an offensive war

it would be a defensive war

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.