Question 111524
Start by assigning a variable to the number you want to find.  Let's call it n.  Now let's write an expression for the relationship that was described.
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First, we need an expression for two thirds of the number.  This is simply {{{(2/3)n}}}.
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Then we need to reduce that amount by 11.  That gives us {{{(2/3)n-11}}}.
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Four more than the number is just {{{n+4}}}.  And finally, the problem tells us that these two quantities are equal, so:
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{{{n+4=(2/3)n-11}}}
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All that is left is to solve the equation for n:
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Add -4 to both sides:
{{{n=(2/3)n-15}}}
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Add -(2/3)n to both sides:
{{{n-(2/3)n=-15}}}
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Combine terms:
{{{(1/3)n=-15}}}
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Multiply both sides by 3:
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{{{n=-45}}}
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Last step -- VERY IMPORTANT -- Check your answer.
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Two thirds of -45 is -30, reduced by 11 is -30 - 11=-41
Four more than -45 is -45 + 4 = -41
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The answer checks!