what is the algebraic expression represents the phrase “the quotient of negative eight and the sum of a number and three”?

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You set it up like this. So quotient means that you're dividing, so put a ÷ Next, it says the dividend, or the part being divided is -8, so now you have this: -8 ÷ Lastly, it says the divisor, or the part doing the dividing, is a quantity equal to the sum of "some number" (we'll use x) and 3. Since the divisor is one quantity collectively, you have to put it in parentheses. This gives you: (x + 3) When you put it all together, you get -8 ÷ (x + 3). This can also be written as a fraction by putting -8 over (x+3).

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