document.write( "Question 559095: Can you please help me understand this one, solve for x. My work is typed below the problem.
\n" ); document.write( "3x-4=1+(x)sqrt(2)
\n" ); document.write( " -1 -1
\n" ); document.write( "3x-5=(x)sqrt(2)
\n" ); document.write( "-3x -3x
\n" ); document.write( "-5=(x)sqrt(2)-3X \n" ); document.write( "
Algebra.Com's Answer #363321 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
So far, so good. You got to
\n" ); document.write( "\"-5=%28x%29sqrt%282%29-3x\" and all your x's are on one side of the equal sign.
\n" ); document.write( "If you had \"2x-3x\" on the right side, you would simplify it to \"-x\",
\n" ); document.write( "because \"2x-3x\" = \"2%2Ax-3%2Ax\" = \"%282-3%29%2Ax\" = \"%28-1%29%2Ax\" = \"-x\"
\n" ); document.write( "You are really applying the distributive property there, but we do not need to explain that much.
\n" ); document.write( "It looks simple and easy with \"2x\".
\n" ); document.write( "With \"sqrt%282%29%2Ax\" it looks more intimidating, but it works just the same way:
\n" ); document.write( "\"sqrt%282%29%2Ax-3%2Ax\" = \"%28sqrt%282%29-3%29%2Ax\".
\n" ); document.write( "So we simplify
\n" ); document.write( "\"x%2Asqrt%282%29-3x=-5\" --> \"%28sqrt%282%29-3%29%2Ax=-5\"
\n" ); document.write( "To find \"x\", we have to divide by \"%28sqrt%282%29-3%29\" both sides of the equation, to get
\n" ); document.write( "\"x=-5%2F%28sqrt%282%29-3%29\"
\n" ); document.write( "There's not much more that can be done, but there are equivalent ways to express it, and you may see another expression as the solution.
\n" ); document.write( "It is customary to convert something like that into an eqivalent expression with no square roots in the denominator. It is called \"rationalizing\". I would do it like this:
\n" ); document.write( "\"x=%28-5%2F%28sqrt%282%29-3%29%29%2A%28%28sqrt%282%29%2B3%29%2F%28sqrt%282%29%2B3%29%29\" --> \"x=-5%28sqrt%282%29%2B3%29%2F%28%28sqrt%282%29-3%29%28sqrt%282%29%2B3%29%29\" --> \"x=-5%28sqrt%282%29%2B3%29%2F%28%28sqrt%282%29%29%5E2-3%5E2%29%29\" --> \"x=-5%28sqrt%282%29%2B3%29%2F%282-9%29%29\" --> \"x=-5%28sqrt%282%29%2B3%29%2F%28-7%29%29\" --> \"x=5%28sqrt%282%29%2B3%29%2F7\"
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