document.write( "Question 798458: Please help me solve the equation: one half a number increased by 16 is four less than 2/3 of the number
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #482273 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
\"x\"= the number
\n" ); document.write( "\"%281%2F2%29x\"= one half the number (optional step)
\n" ); document.write( "\"%281%2F2%29x%2B16\"= one half the number increased by 16 (optional step)
\n" ); document.write( "\"%282%2F3%29x\"= 2/3 of the number (optional step)
\n" ); document.write( "\"%282%2F3%29x-4\"= four less than 2/3 of the number (optional step)
\n" ); document.write( "
\n" ); document.write( "The problem says (translates into)
\n" ); document.write( "\"%281%2F2%29x%2B16=%282%2F3%29x-4\"
\n" ); document.write( "
\n" ); document.write( "We could work with fractions, or eliminate denominators.
\n" ); document.write( "
\n" ); document.write( "Working with fractions:
\n" ); document.write( "\"%281%2F2%29x%2B16=%282%2F3%29x-4\"
\n" ); document.write( "\"16%2B4=%282%2F3%29x-%281%2F2%29x\" (Do you need to do this in 2 steps?)
\n" ); document.write( "\"20=%282%2F3-1%2F2%29x\"
\n" ); document.write( "\"20=%284%2F6-3%2F6%29x\" (optional step)
\n" ); document.write( "\"20=%281%2F6%29x\"
\n" ); document.write( "\"6%2A20=6%2A%281%2F6%29x\" (optional step)
\n" ); document.write( "\"120=1%2Ax\" (optional step)
\n" ); document.write( "\"highlight%28x=120%29\"
\n" ); document.write( "
\n" ); document.write( "Eliminating denominators:
\n" ); document.write( "From \"%281%2F2%29x%2B16=%282%2F3%29x-4\",
\n" ); document.write( "we multiply the expressions on both sides of the equal sign times 6 to get
\n" ); document.write( "\"6%2A%28%281%2F2%29x%2B16%29=6%2A%28%282%2F3%29x-4%29\" (optional step)
\n" ); document.write( "\"6%2A%281%2F2%29x%2B6%2A16=6%2A%282%2F3%29x-6%2A4\" (optional step)
\n" ); document.write( "\"3x%2B96=4x-24\"
\n" ); document.write( "\"96%2B24=4x-3x\" (Do you need to do this in 2 steps?)
\n" ); document.write( "\"120=%284-3%29x\" (optional step)
\n" ); document.write( "\"120=1%2Ax\" (optional step)
\n" ); document.write( "\"highlight%28x=120%29\"
\n" ); document.write( "
\n" ); document.write( "(Number of steps will vary with teacher and student preference).
\n" ); document.write( "
\n" );