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Algebra 1 help...

That would be 2x + 3(x+1).

edit: your second response makes no sense, that would just be "Eight times the integer" as x/1 = x, methinks.

2nd edit: You changed it. 😛 Second response is still wrong -- it's a word problem, so read left to right. If they wanted the entire equation to be multiplied by two, they would've added it at the end.
 
What is the product of twice the integer added to three times the next consecutive integer?

I disagree with the other responses. It says "what is the product of ... times ...", meaning it would be the product of the elements listed before the "times" and after the "times". This would make it:

(2x + 3)(x + 1)

Then again, it could be interpreted as others have interpreted it. It is too vague to tell with certainty.
 
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