document.write( "Question 202031: Which of the following is true? A) The equation 3x=x has no solution. B)The solution to x/x-4=4/x-4 is x=4. C)There are two solutions for /3x-1/=9. D)Some linear equations can only be solved with a graphing utility. stumped. please help. \n" ); document.write( "

Algebra.Com's Answer #152287 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
A)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x=x\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x-x=0\"$ Subtract $\"x\"$ from both sides.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2x=0\"$ Combine like terms on the left side.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=%280%29%2F%282%29\"$ Divide both sides by $\"2\"$ to isolate $\"x\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=0\"$ Reduce.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the solution is $\"x=0\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the statement \"The equation 3x=x has no solution\" is false (since it does have a solution).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "B) \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2F%28x-4%29=4%2F%28x-4%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"4%2F%284-4%29=4%2F%284-4%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"4%2F0=4%2F0\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since division by zero is undefined, this means that x=4 CANNOT be a solution. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the statement \")The solution to x/x-4=4/x-4 is x=4.\" is false.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "C)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"abs%283x-1%29=9\"$ Start with the given equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Break up the absolute value (remember, if you have $\"abs%28x%29=a\"$ , then $\"x=-a\"$ or $\"x=a\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x-1=-9\"$ or $\"3x-1=9\"$ Set the expression $\"3x-1\"$ equal to the original value 9 and it's opposite -9\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now lets focus on the first equation $\"3x-1=-9\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x=-9%2B1\"$ Add 1 to both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x=-8\"$ Combine like terms on the right side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=%28-8%29%2F%283%29\"$ Divide both sides by 3 to isolate x\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=-8%2F3\"$ Reduce\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now lets focus on the second equation $\"3x-1=9\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x=9%2B1\"$ Add 1 to both sides\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"3x=10\"$ Combine like terms on the right side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=%2810%29%2F%283%29\"$ Divide both sides by 3 to isolate x\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=10%2F3\"$ Reduce\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the solutions to $\"abs%283x-1%29=9\"$ are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=-8%2F3\"$ and $\"x=10%2F3\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since there are two solutions, the statement \"There are two solutions for /3x-1/=9\" is true.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "D)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Because you can solve ANY linear equation with a graph, I would argue that the statement \"Some linear equations can only be solved with a graphing utility\" is false. If the \"some\" was changed to \"all\", then it would true.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: I'm talking about approximate solutions. If the book means exact solutions, then the answer changes. \n" ); document.write( "

\n" );