document.write( "Question 62560: how do you solve 2*3(4+5-3/4(5+7-3))+5 \n" ); document.write( "
Algebra.Com's Answer #43364 by Edwin McCravy(20054) $\"\"$ $\"About$
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how do you solve  2*3(4+5-3/4(5+7-3))+5\r\n" );
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document.write( "You evaluate expressions, you don't \"solve\" them. (You solve equations.)\r\n" );
document.write( "This is not an equation because there is no equal sign.  So you should\r\n" );
document.write( "have asked \"How do you EVALUATE  2*3(4+5-3/4(5+7-3))+5\r\n" );
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document.write( "The priorities are \r\n" );
document.write( "1. Work within first innermost parentheses, if any, using the\r\n" );
document.write( "   following priorities, or of if none, use the following \r\n" );
document.write( "   priorities on the expression:\r\n" );
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document.write( "2. Do the first exponent, going left to right.\r\n" );
document.write( "3. Do the first multiplication or division, going left to right.\r\n" );
document.write( "4. Do the first addition or subtraction, going left to right.  \r\n" );
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document.write( "Place understood multiplication symbols between the 3 and the (, \r\n" );
document.write( "and between the 4 and the (.\r\n" );
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document.write( " 2*3*(4+5-3/4*(5+7-3))+5\r\n" );
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document.write( "Look for the innermost parentheses, which is\r\n" );
document.write( "             (5+7-3)\r\n" );
document.write( "There are no exponents or multiplication in the innermost \r\n" );
document.write( "parentheses, so we go to the first addition or subtraction, \r\n" );
document.write( "going left to right.  This is\r\n" );
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document.write( "              5+7\r\n" );
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document.write( "So we replace the 5+7 by 12, and now we have:\r\n" );
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document.write( " 2*3*(4+5-3/4*(12-3))+5\r\n" );
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document.write( "Now we start over.  The innermost parentheses is (12-3).\r\n" );
document.write( "There are no exponents, multiplication, or division\r\n" );
document.write( "within this parentheses, so we go to the first addition\r\n" );
document.write( "or subtraction within it.  This is\r\n" );
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document.write( "              12-3\r\n" );
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document.write( "So we replace the 12-3 by 9, and now we have \r\n" );
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document.write( "     2*3*(4+5-3/4*(9))+5\r\n" );
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document.write( "Now we can eliminate the innermost parentheses, since\r\n" );
document.write( "there is only one number within it. So now we have\r\n" );
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document.write( "     2*3*(4+5-3/4*9)+5\r\n" );
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document.write( "Now we start over.  The innermost parentheses is\r\n" );
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document.write( "         (4+5-3/4*9)\r\n" );
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document.write( "There are no exponents within that parentheses, So we\r\n" );
document.write( "look for the first multiplication or division going left\r\n" );
document.write( "to right.  The first one we come to is the division \r\n" );
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document.write( "             3/4\r\n" );
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document.write( "So we replace the 3/4 by 0.75, and now we have:\r\n" );
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document.write( "     2*3*(4+5-0.75*9)+5\r\n" );
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document.write( "Now we start over.  The innermost parentheses is\r\n" );
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document.write( "        (4+5-0.75*9)\r\n" );
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document.write( "There are no exponents within that parentheses, So we\r\n" );
document.write( "look for the first multiplication or division going left\r\n" );
document.write( "to right.  The first one we come to is the multiplication\r\n" );
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document.write( "             0.75*9\r\n" );
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document.write( "So we replace the 0.75*9 by 6.75. Now we have\r\n" );
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document.write( "      2*3*(4+5-6.75)+5\r\n" );
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document.write( "Now we start over.  The innermost parentheses is\r\n" );
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document.write( "         (4+5-6.75)\r\n" );
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document.write( "There are no exponents within that parentheses, nor\r\n" );
document.write( "any multiplications or divisions. So we look for\r\n" );
document.write( "the first addition or subtraction going left\r\n" );
document.write( "to right.  The first one we come to is the addition\r\n" );
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document.write( "          4+5\r\n" );
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document.write( "So we replace the 4+5 by 9. Now we have\r\n" );
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document.write( "       2*3*(9-6.75)+5\r\n" );
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document.write( "Now we start over.  The innermost parentheses is\r\n" );
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document.write( "           (9-6.75)\r\n" );
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document.write( "There are no exponents within that parentheses, nor\r\n" );
document.write( "any multiplications or divisions. So we look for\r\n" );
document.write( "the first addition or subtraction going left\r\n" );
document.write( "to right.  The first one (only one) we come to is the \r\n" );
document.write( "subtraction 9-6.75.  So we replace the 9-6.75 by\r\n" );
document.write( "2.25. Now we have\r\n" );
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document.write( "       2*3*(2.25)+5\r\n" );
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document.write( "Now we start over.  Since there is only one number \r\n" );
document.write( "inside the parentheses we can dispense with the \r\n" );
document.write( "parentheses, and now we have\r\n" );
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document.write( "       2*3*2.25+5\r\n" );
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document.write( "Now we start over. There are no parentheses nor \r\n" );
document.write( "exponents, so we look for the first multiplication \r\n" );
document.write( "or division going left to right.  This is 2*3, \r\n" );
document.write( "so we replace the 2*3 by 6, and have\r\n" );
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document.write( "         6*2.25+5\r\n" );
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document.write( "Now we start over. There are no parentheses nor \r\n" );
document.write( "exponents, so we look for the first multiplication \r\n" );
document.write( "or division going left to right.  This is 6*2.25, \r\n" );
document.write( "so we replace the 6*2.25 by 13.5, and have\r\n" );
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document.write( "         13.5+5\r\n" );
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document.write( "The only thing left is that one addition, so the\r\n" );
document.write( "final result is\r\n" );
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document.write( "         18.5 \r\n" );
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document.write( "Edwin
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