Question 119683
Put the given words into an equation. Let x be the first even integer. Then x+2 is the next even integer (since you need to add 2 to a given even number to get the next even number), and x+4 is the next even integer:
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{{{x(x+2)=9(x+4)-6}}}
Multiply through:
{{{x^2+2x=9x+36-6}}}
Put the quadratic into standard form:
{{{x^2-7x-30=0}}}
Factor:
{{{(x+3)(x-10)=0}}}
Solve for x:
{{{x+3=0}}}
{{{x=-3}}}
Note that this value for x is no good for this problem, since it is an odd number.
{{{x-10=0}}}
{{{highlight(x=10)}}}
Remember, x is the first even integer. So the three even integers are:
{{{10}}},{{{12}}},{{{14}}}
You can verify this result to see if the given holds true with these numbers.
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Good Luck,
tutor_paul@yahoo.com