document.write( "Question 882183: for each of the following find the value of x which will make the statement true
\n" ); document.write( "1. x over 7 - x = 12
\n" ); document.write( "2. x+2x over 6 - 3 =0\r
\n" ); document.write( "\n" ); document.write( "3. 7x - 1
\n" ); document.write( "-------- = 2-3x
\n" ); document.write( " 4 ----------
\n" ); document.write( " 5\r
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\n" ); document.write( "\n" ); document.write( "4. x over 4 - 2x +1 over 6 = -2
\n" ); document.write( "5. 2(x+5) over 3 + x over 4 = 2 over 3\r
\n" ); document.write( "\n" ); document.write( "'over' means that its a fraction just so you know
\n" ); document.write( "can you please show me how you worked it out because I have no idea
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Algebra.Com's Answer #532748 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
NOTE 1: I will try to show the work baby step by baby step.
\n" ); document.write( "It may be way too babyish for the level you are at,
\n" ); document.write( "so feel free to skip baby steps you do not need.
\n" ); document.write( "
\n" ); document.write( "NOTE 2: You are more likely to get help and for that help to be answers to the right questions
\n" ); document.write( "if you use a way to write math that communicates what you mean more clearly.
\n" ); document.write( "I will be guessing what you mean a lot, so if I did not guess right, ask again, in a clearer way.
\n" ); document.write( "Here are some commonly used symbols:
\n" ); document.write( "* is the times sign, as in writing 3*5 for 3 times 5.
\n" ); document.write( "/ is the \"over\" or dividing symbol as in 35/7=5 for 35 divided by 7 equals 5, or
\n" ); document.write( "x/(7-x) for \"x%2F%287-x%29\" , or (7x-1)/4=(2x-3)/5 for \"%287x-1%29%2F4=%282x-3%29%2F5\" .
\n" ); document.write( "When writing with pen and paper, that horizontal line meaning \"over\" is a great ink-saver.
\n" ); document.write( "In the conventional algebra language,
\n" ); document.write( "that horizontal line means that the expressions above and below the line are calculated first, before dividing,
\n" ); document.write( "and you do not need to write the parentheses.
\n" ); document.write( "When typing, if there is an expression above (or below) that horizontal line that you read as \"over\",
\n" ); document.write( "you have to wrap that expression in parentheses.
\n" ); document.write( "Examples:
\n" ); document.write( "x/(7-x) means \"x%2F%287-x%29\" , but x/7-x means \"x%2F7-x\"
\n" ); document.write( "Also, according to the conventions (rules) on \"order of operations\",
\n" ); document.write( "(x+2x)/6 - 3 =\"%28x%2B2x%29%2F6+-+3\" , but x+2x/6 - 3 =\"x%2B2x%2F6+-+3\" , and (x+2x)/(6 - 3) =\"%28x%2B2x%29%2F%286+-+3%29\"\r
\n" ); document.write( "\n" ); document.write( "1. Did you mean \"x%2F%287-x%29=12\" ?
\n" ); document.write( "In that case, multiply both sides of the equal sign times \"%287-x%29\" to get
\n" ); document.write( "\"x%287-x%29%2F%287-x%29=12%287-x%29\"
\n" ); document.write( "Simplify on the left side and apply the distributive property on the right side to get
\n" ); document.write( "\"x=84-12x\"
\n" ); document.write( "Add \"12x\" to both sides of the equal sign, and simplify to get
\n" ); document.write( "\"x%2B12x=84-12x%2B12x\" ---> \"1x%2B12x=84\" ---> \"%281%2B12%29x=84\" ---> \"13x=84\"
\n" ); document.write( "Now, divide both sides by \"13\" and simplify to get
\n" ); document.write( "\"13x%2F13=84%2F13\" ---> \"x=84%2F3\"
\n" ); document.write( "OR did you mean \"x%2F7-x=12\" ?
\n" ); document.write( "In that case, multiply both sides of the equal sign times \"%287-x%29\" to get
\n" ); document.write( "\"7%28x%2F7-x%29=7%2A12\"-->\"7x%2F7-7x=84\"-->\"1x-7x=84\"-->\"%281-7%29x=84\"-->\"%28-6%29x=84\"
\n" ); document.write( "Now, dividing both sides by \"%28-6%29\" and simplifying, you get
\n" ); document.write( "\"%28-6%29x%2F%28-6%29=84%2F%28-6%29\"-->\"x=-84%2F6\"-->\"x=-14\"
\n" ); document.write( "
\n" ); document.write( "2. I am guessing that you meant x+2x/6-3=0, which is \"x%2B2x%2F6-3=0\" .
\n" ); document.write( "That may not be what you meant, but I thought it was a good guess.
\n" ); document.write( "\"x%2B2x%2F6-3=0\"
\n" ); document.write( "I would simplify \"2x%2F6\" first.
\n" ); document.write( "Then, and in general, it is good to get rid of denominators by multiplying both sides of the equal sign times a cleverly chosen number or expression.
\n" ); document.write( "\"x%2Bx%2F3-3=0\"--->\"3%28x%2Bx%2F3-3%29=3%2A0\"--->\"3x%2B3x%2F3-3%2A3=0\"--->\"3x%2Bx-9=0\"
\n" ); document.write( "(Most people would just write the last equation, and skip the in-between steps). \"3x%2Bx-9=0\"--->\"4x-9=0\"--->\"4x-9%2B9=0%2B9\"--->\"4x=9\"--->\"x=9%2F4\"\r
\n" ); document.write( "\n" ); document.write( "3. I am guessing that you meant (7x-1)/4=(2-3x)/5 , which is \"%287x-1%29%2F4=%282-3x%29%2F5\" .
\n" ); document.write( "In that case, I would first multiply both sides of the equal sign times \"4%2A5=20\" :
\n" ); document.write( "\"20%287x-1%29%2F4=20%282-3x%29%2F5\"--->\"5%287x-1%29=4%282-3x%29\"--->\"35x-5=8-12x%29\"
\n" ); document.write( "That got rid of denominators.
\n" ); document.write( "\"35x-5=8-12x%29\"--->\"35x-5%2B5=8-12x%2B5%29\"--->\"35x=13-12x%29\"--->\"35x%2B12x=13-12x%2B12x%29\"--->\"47x=13%29\"--->\"47x%2F47=13%2F47%29\"
\n" ); document.write( "--->\"x=13%2F47%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4. I am guessing that you meant x/4 - (2x +1)/6 = -2, which is \"x%2F4+-+%282x+%2B1%29%2F6+=+-2\"
\n" ); document.write( "I would start by multiplying both sides of the equal sign times \"12\" , which is a multiple of \"4\" and \"6\" , and is smaller than \"4-6=24\" .
\n" ); document.write( "\"12%28x%2F4+-+%282x+%2B1%29%2F6%29=12%2A%28-2%29\"
\n" ); document.write( "\"12x%2F4+-+12%282x+%2B1%29%2F6%29=-24\"
\n" ); document.write( "\"3x+-+2%282x+%2B1%29=-24\"
\n" ); document.write( "\"3x+-+4x+-2=-24\"
\n" ); document.write( "\"3x+-+4x+-2%2B2=-24%2B2\"
\n" ); document.write( "\"3x+-+4x=-22\"
\n" ); document.write( "\"%283-4%29x=-22\"
\n" ); document.write( "\"%28-1%29x=-22\"
\n" ); document.write( "\"%28-1%29x%2F%28-1%29=-22%2F%28-1%29\"
\n" ); document.write( "\"x=22\"
\n" ); document.write( "
\n" ); document.write( "5. \"2%28x%2B5%29%2F3+%2B+x%2F4+=+2%2F3\"
\n" ); document.write( "I would start by multiplying both sides of the equal sign times \"3%2A4=12\"
\n" ); document.write( "\"12%2A2%28x%2B5%29%2F3+%2B+12x%2F4+=+12%2A2%2F3\"
\n" ); document.write( "\"8%28x%2B5%29+%2B+3x=+8\"
\n" ); document.write( "\"8x%2B40+%2B+3x=+8\"
\n" ); document.write( "\"8x%2B40+-40%2B+3x=+8-40\"
\n" ); document.write( "\"8x%2B+3x=+-36\"
\n" ); document.write( "\"%288%2B3%29x=+-36\"
\n" ); document.write( "\"11x=+-36\"
\n" ); document.write( "\"11x%2F11=+-36%2F11\"
\n" ); document.write( "\"x=+-36%2F11\"
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