document.write( "Question 339198: How do I solve this absolute value equation:3/5+2|2-3/4x|=7. The answers are -8/5 or 104/15 but I do not know how the answers are found. Please reply ASAP. Thanks. \n" ); document.write( "
Algebra.Com's Answer #243115 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"3%2F5%2B2%2Aabs%282-%283%2F4%29x%29=7\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"2%2Aabs%282-%283%2F4%29x%29=7-3%2F5\" Subtract \"3%2F5\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"2%2Aabs%282-%283%2F4%29x%29=32%2F5\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "\"abs%282-%283%2F4%29x%29=%2832%2F5%29%281%2F2%29\" Multiply both sides by \"1%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "\"abs%282-%283%2F4%29x%29=32%2F10\" Multiply.\r
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\n" ); document.write( "\n" ); document.write( "\"abs%282-%283%2F4%29x%29=16%2F5\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "Now remember that if \"abs%28x%29=a\", then \"x=a\" or \"x=-a\"\r
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\n" ); document.write( "\n" ); document.write( "This means that if \"abs%282-%283%2F4%29x%29=16%2F5\", then \"2-%283%2F4%29x=16%2F5\" or \"2-%283%2F4%29x=-16%2F5\"\r
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\n" ); document.write( "\n" ); document.write( "Let's solve the first equation:\r
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\n" ); document.write( "\n" ); document.write( "\"2-%283%2F4%29x=16%2F5\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"20%282-%283%2Fcross%284%29%29x%29=20%2816%2Fcross%285%29%29\" Multiply both sides by the LCD \"20\" to clear any fractions.\r
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\n" ); document.write( "\n" ); document.write( "\"40-15x=64\" Distribute and multiply.\r
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\n" ); document.write( "\n" ); document.write( "\"-15x=64-40\" Subtract \"40\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"-15x=24\" Combine like terms on the right side.\r
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\n" ); document.write( "\n" ); document.write( "\"x=%2824%29%2F%28-15%29\" Divide both sides by \"-15\" to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( "\"x=-8%2F5\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So one solution is \"x=-8%2F5\" \r
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\n" ); document.write( "\n" ); document.write( "Now let's solve \"2-%283%2F4%29x=-16%2F5\"\r
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\n" ); document.write( "\n" ); document.write( "\"2-%283%2F4%29x=-16%2F5\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"20%282-%283%2Fcross%284%29%29x%29=20%28-16%2Fcross%285%29%29\" Multiply both sides by the LCD \"20\" to clear any fractions.\r
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\n" ); document.write( "\n" ); document.write( "\"40-15x=-64\" Distribute and multiply.\r
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\n" ); document.write( "\n" ); document.write( "\"-15x=-64-40\" Subtract \"40\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"-15x=-104\" Combine like terms on the right side.\r
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\n" ); document.write( "\n" ); document.write( "\"x=%28-104%29%2F%28-15%29\" Divide both sides by \"-15\" to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( "\"x=104%2F15\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So another solution is \"x=104%2F15\" \r
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\n" ); document.write( "\n" ); document.write( "This means that the solutions to \"3%2F5%2B2%2Aabs%282-%283%2F4%29x%29=7\" are \"x=-8%2F5\" or \"x=104%2F15\" \r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my tutoring website. \r
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\n" ); document.write( "\n" ); document.write( "Jim
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