Question 182113
Let x = smaller even number.  That means (x + 2) will be the next consecutive even number (aka. 'larger' in the word problem).
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Now, write the statements down in equation form (substitute x and (x+2) in place of the two numbers):
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"Three times the smaller of two consecutive even integers is added to the larger,":
  3x + (x + 2)
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"The result is 4 more than 3 times the larger.":
  = 4 + (3 * (x + 2) )
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So putting it all together we have:
  3x + (x + 2) = 4 + (3 * (x + 2))
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Simplifying (remember to multiply the '3' by both the 'x' and the '2' on the right hand side):
  4x + 2 = 4 + 3x + 6
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Gathering the x's on the left (subtract 3x from both sides):
  1x + 2 = 10
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Subtracting 2 from both sides gives us <b>x = 8</b>, which represents the smaller even number.  Given that, we know that the next consecutive even number would be <b>10</b>.