document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88061>Question 88061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how can i solve this equation for x and check my result ..please help\r<BR>\n" );
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document.write( "7(3x + 4) =8(2x +5) + 13 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64043 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=64043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "7(3x + 4) =8(2x +5) + 13<BR>\n" );
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document.write( "To solve this equation, first do the distributed multiplications on the left and right sides ...<BR>\n" );
document.write( "that is multiply the 7 times both the 3x and the +4 and on the right side multiply the 8 by<BR>\n" );
document.write( "the 2x and the +5.  When you do those two multiplications you get:<BR>\n" );
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document.write( "21x + 28 = 16x + 40 + 13<BR>\n" );
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document.write( "The next goal will be to get all the terms containing x on the left side of the equation.<BR>\n" );
document.write( "You can do this by recognizing that you need to get rid of the 16x on the right side. Do <BR>\n" );
document.write( "that by subtracting 16x from the right side. But in an equation, if you subtract 16x from<BR>\n" );
document.write( "one side then you must also subtract 16x from the other side. This makes the<BR>\n" );
document.write( "equation become:<BR>\n" );
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document.write( "21x - 16x + 28 = 16x - 16x + 40 + 13<BR>\n" );
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document.write( "On the right side the 16x and the -16x cancel each other so the equation reduces to:<BR>\n" );
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document.write( "21x - 16x + 28 = 40 + 13<BR>\n" );
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document.write( "The next goal is to get all the numbers on the right side of the equation.  You can do that<BR>\n" );
document.write( "by getting rid of the 28 on the left side of the equation, and that is done by subtracting 28<BR>\n" );
document.write( "from both sides.  Subtracting 28 from both sides results in:<BR>\n" );
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document.write( "21x - 16x + 28 - 28 = 40 + 13 - 28<BR>\n" );
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document.write( "On the left side the 28 and the -28 cancel each other out and the equation then becomes:<BR>\n" );
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document.write( "21x - 16x = 40 + 13 - 28<BR>\n" );
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document.write( "Now combine the terms on both sides.  On the left side when you subtract 16x from 21x, the<BR>\n" );
document.write( "result is 5x. And on the right side, when you add 40 plus 13 and then subtract 28 the<BR>\n" );
document.write( "result is 25. This means the equation becomes:<BR>\n" );
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document.write( "5x = 25<BR>\n" );
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document.write( "Now you can solve for x by dividing both sides by 5 which is the multiplier of x. This<BR>\n" );
document.write( "reduces the equation to:<BR>\n" );
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document.write( "x = 5<BR>\n" );
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document.write( "You now have the answer for x. To check, go back to the original equation and substitute 5 <BR>\n" );
document.write( "in the place of x and see if both sides of the equation are equal to each other.<BR>\n" );
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document.write( "The original equation was:<BR>\n" );
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document.write( "7(3x + 4) =8(2x +5) + 13<BR>\n" );
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document.write( "Replacing x with 5 results in:<BR>\n" );
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document.write( "7(3*5 + 4) = 8(2*5 + 5) + 13<BR>\n" );
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document.write( "Do the multiplications of the terms inside the parentheses to get:<BR>\n" );
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document.write( "7(15 + 4) = 8(10 + 5) + 13<BR>\n" );
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document.write( "Add the numbers inside the parentheses:<BR>\n" );
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document.write( "7(19) = 8(15) + 13<BR>\n" );
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document.write( "Multiply 7 times 19 and 8 times 15 to get:<BR>\n" );
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document.write( "133 = 120 + 13<BR>\n" );
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document.write( "Add the two numbers on the right side:<BR>\n" );
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document.write( "122 = 133<BR>\n" );
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document.write( "When x equals 5 both sides of the equation equal 133, so the equation works when x = 5. <BR>\n" );
document.write( "Therefore, the answer of x = 5 is correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to apply some basic rules for solving equations.\r<BR>\n" );
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