document.write( "Question 1012038: [(X-4)/3]-[3/(X-4)]>(1/3)X \n" ); document.write( "

Algebra.Com's Answer #627869 by ValorousDawn(53) $\"\"$ $\"About$

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Move all the terms to the left side. You now have
\n" ); document.write( " $\"%28%28x-4%29%2F3%29-%283%2F%28x-4%29%29-%28x%2F3%29%3E0\"$
\n" ); document.write( "Put all the terms over a common denominator. Your \"prime\" factors are 3 and (x-4) so your common denominator is 3(x-4).
\n" ); document.write( " $\"%28%28X-4%29%5E2%2F3%28x-4%29%29-%289%2F3%28X-4%29%29-x%28x-4%29%2F3%28x-4%29%3E0\"$
\n" ); document.write( "Simplify and combine like terms.
\n" ); document.write( " $\"%28-4x%2B7%29%2F%283%28x-4%29%29\"$
\n" ); document.write( "Find critical points. They are -7/4 and 4. Since the leading coefficient of the entire function is negative, the end term behavior is negative. You switch signs every crossing of critical point, and as such, the only time you have a positive result is the desired interval. Since it's strictly greater than\r
\n" ); document.write( "\n" ); document.write( "[-7/4, 4] \n" ); document.write( "

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