Question 91042
A couple of ways come to mind on this problem.
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You are given:
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{{{n+4/9=3}}}
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To solve for n, you might replace the 3 on the right side by {{{27/9}}} which is equal to 3.
Note that this fraction has the same denominator as the fraction on the left side.
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Next you can get rid of the {{{4/9}}} on the left side by subtracting {{{4/9}}} from both 
sides.  This subtraction results in:
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{{{n = 27/9 - 4/9}}}
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Because the fractions on the right side have the same denominator you can subtract their
numerators and the equation reduces to:
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{{{n = (27-4)/9 = 23/9}}}
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So, you have the answer of {{{n = 23/9}}}
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Another way you could do the problem is to start with the original equation:
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{{{n+4/9=3}}}
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and get rid of the denominator 9 by multiplying both sides (all terms) by 9. This multiplication
results in:
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{{{9n + (9*4)/9 = 9*3}}}
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And this simplifies to:
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{{{9n + 4 = 27}}}
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Subtract 4 from both sides and you have:
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{{{9n = 23}}}
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And finally, solve for n by dividing both sides by 9 (the multiplier of n) to get:
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{{{n = 23/9}}}
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Which is the same answer as we got before.
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You can check the answer by returning to the original equation you were given and substituting
{{{23/9}}} for n to get:
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{{{23/9 + 4/9 = 3}}}
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On the left side, there is a common denominator so the numerators can be added to get:
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{{{(23+4)/9 = 3}}}
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After the numerators are added you have:
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{{{27/9 = 3}}}
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And after the 27 is divided by the 9 on the left side you get:
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{{{3 = 3}}}
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Since this is true, the equation works when {{{n = 23/9}}}. Therefore, the answer we 
got is correct.
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Hope this helps you to understand the problem and several ways in which it can be worked.
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And just in case you meant the problem to be:
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{{{(n + 4)/9 = 3}}}
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(which is not the way you wrote it), you can work this problem by multiplying both sides
by 9 (all terms) to make the equation become:
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{{{n + 4 = 27}}}
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Then subtract 4 from both sides and you get:
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{{{n = 27 - 4 = 23}}}
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In this case the answer for n is n = 23.