document.write( "Question 737197: Which of the following inequalities is true for all real numbers?
\n" ); document.write( "x^3 > or equal to x^2
\n" ); document.write( "3x^2 > or equal to 2x^3
\n" ); document.write( "(2x)^2 > or equal to 3x^2
\n" ); document.write( "3(x-2)^2 > or equal to 3x^2 - 2 \n" ); document.write( "

Algebra.Com's Answer #450210 by fcabanski(1391) $\"\"$ $\"About$

You can put this solution on YOUR website!
Simplify/solve each one using algebra.

\n" ); document.write( " $\"x%5E3+%3E=+x%5E2\"$ Divide both sides by $\"x%5E2\"$

\n" ); document.write( " $\"x%3E=+1\"$ That's only true for real numbers 1 or greater.

\n" ); document.write( " $\"3x%5E2+%3E=+2x%5E3\"$ Divide both sides by $\"x%5E2\"$ and divide both sides by 2.

\n" ); document.write( " $\"3%2F2+%3E=+x\"$ Only true for real numbers less than or equal to 3/2.

\n" ); document.write( " $\"%282x%29%5E2+%3E=+3x%5E2\"$

\n" ); document.write( " $\"4x%5E2+%3E=+3x%5E2\"$ Divide both sides by $\"x%5E2\"$

\n" ); document.write( " $\"4+%3E=+3\"$ That's always true.

\n" ); document.write( " $\"3%28x-2%29%5E2+%3E=+3x%5E2+-+2\"$

\n" ); document.write( " $\"3x%5E2+-+12x+%2B12+%3E=+3x%5E2+-+2\"$

\n" ); document.write( " $\"-12x+%3E=+-14\"$

\n" ); document.write( " $\"x%3E=+7%2F6\"$ Not true for all real numbers.
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Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
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