document.write( "Question 504571: please help can not understand if I am doing this right. Thank you so much
\n" ); document.write( "Sovlve the equation:
\n" ); document.write( "4 - 8x = 8
\n" ); document.write( " x +1 = x +1 \r
\n" ); document.write( "\n" ); document.write( "Here's what I did\r
\n" ); document.write( "\n" ); document.write( "4(x + 2)= 8
\n" ); document.write( "(x +1)(x -1) = x + 1 \n" ); document.write( "
Algebra.Com's Answer #339649 by Theo(13342)\"\" \"About 
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you have 4 - 8x = 8
\n" ); document.write( "subtract 4 from both sides of that equation to get:
\n" ); document.write( "-8x = 8 - 4 which becomes:
\n" ); document.write( "-8x = 4
\n" ); document.write( "multiply both sides of the equation by -2 to get:
\n" ); document.write( "8x = -4
\n" ); document.write( "divide both sides of the equation by 8 to get:
\n" ); document.write( "x = -4/8
\n" ); document.write( "this reduces to:
\n" ); document.write( "x = -1/2
\n" ); document.write( "substitute for x in the original equation of:
\n" ); document.write( "4 - 8x = 8 to get:
\n" ); document.write( "4 - 8(-1/2) = 8 which becomes:
\n" ); document.write( "4 - (-8/2) = 8 which becomes:
\n" ); document.write( "4 + 8/2 = 8 which becomes:
\n" ); document.write( "4 + 4 = 8 which is true, so the value of x = -1/2 is good.\r
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\n" ); document.write( "\n" ); document.write( "your second equation is:
\n" ); document.write( "x+1 = x+1
\n" ); document.write( "subtract x from both sides of the equation to get:
\n" ); document.write( "x - x + 1 = 1
\n" ); document.write( "subtract 1 from both sides of the equation to get:
\n" ); document.write( "x - x = 1 - 1
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "0 = 0
\n" ); document.write( "the variable x dropped out of the equation and the equation is still true so the original equation is an identity and any value of x will satisfy it.\r
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\n" ); document.write( "\n" ); document.write( "when you're solving equations, whatever you do to the left side of the equation has to be done to the right side of the equation as well.\r
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\n" ); document.write( "\n" ); document.write( "the purpose is to isolate the unknown variable to one side of the equation with all the rest on the other side of the equation.\r
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\n" ); document.write( "\n" ); document.write( "you were able to do that with the first problem.\r
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\n" ); document.write( "\n" ); document.write( "you tried to do that with the second problem but the variable disappeared.\r
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\n" ); document.write( "\n" ); document.write( "that's ok.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "if the variable disappears and the equation is true (3 = 3, 0 = 0, etc), then any value of x will solve the equation.\r
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\n" ); document.write( "\n" ); document.write( "if the variable disappears and the equation is false (3 = 2, 0 = 15), etc), then no value of x will solve the equation.\r
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\n" ); document.write( "\n" ); document.write( "an example of an invalid equation would be:
\n" ); document.write( "x+1 x+5
\n" ); document.write( "subtract x from both sides of this equation to get:
\n" ); document.write( "1 = 5
\n" ); document.write( "this is clearly not true, so the equation is invalid and no value of x will satisfy it.
\n" ); document.write( " \n" ); document.write( "
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