document.write( "Question 167310: how do you find \"x\" in a equation like\r
\n" ); document.write( "\n" ); document.write( "2x-3=5x+12\r
\n" ); document.write( "\n" ); document.write( "???
\n" ); document.write( "

Algebra.Com's Answer #123224 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
you want to get all your x's on the same side of the equation.
\n" ); document.write( "you do this by any of the following:
\n" ); document.write( "1. add or subtract the same value to both sides of the equation.
\n" ); document.write( "2. multiply or divide each side of the equation by the same value.
\n" ); document.write( "3. raise both sides of the equation by the same power.
\n" ); document.write( "all of these operations, if done properly, do not change the value of the equation.
\n" ); document.write( "-----
\n" ); document.write( "in your problem, you start off with:
\n" ); document.write( "2x-3 = 5x + 12
\n" ); document.write( "you want to move all your x's to the left side of the equation or the right side of the equation.
\n" ); document.write( "let's try the right.
\n" ); document.write( "you subtract 2x from both sides of the equation.
\n" ); document.write( "2x - 3 - 2x = 5x - 2x + 12.
\n" ); document.write( "when you combine like terms, the 2x on the left side of the equation cancels out.
\n" ); document.write( "combining like terms, you get:
\n" ); document.write( "-3 = 3x + 12.
\n" ); document.write( "now you want to move the 12 from the right side of the equation to the left side.
\n" ); document.write( "you do this by subtracting 12 from both sides of the equation.
\n" ); document.write( "-3 - 12 = 3x + 12 - 12.
\n" ); document.write( "when you combine like terms, the 12 on the right side of the equation cancels out.
\n" ); document.write( "combine like terms, you get:
\n" ); document.write( "-15 = 3x
\n" ); document.write( "now you need to divide both sides of the equation by 3.
\n" ); document.write( "-15 / 3 = 3x / 3
\n" ); document.write( "completing the operation, you get:
\n" ); document.write( "-5 = x
\n" ); document.write( "this is the same as:
\n" ); document.write( "x = -5
\n" ); document.write( "that should be your answer.
\n" ); document.write( "substituting -5 for x in your original equation gets:
\n" ); document.write( "2x-3=5x+12
\n" ); document.write( "(2*-5) - 3 = (5*-5) + 12
\n" ); document.write( "-10 - 3 = -25 + 12
\n" ); document.write( "-13 = -13
\n" ); document.write( "since the 2 sides of the equatin are equal, the value of x = -5 is true.
\n" ); document.write( "-----
\n" ); document.write( "
\n" );