document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=533695>Question 533695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve for x on the following equations. I honestly don't know what to do.\r<BR>\n" );
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document.write( "1).2x+4=28<BR>\n" );
document.write( "2).17x-42=-39<BR>\n" );
document.write( "3).7x-2=5x+10<BR>\n" );
document.write( "4).3x-1-x=3x+5<BR>\n" );
document.write( "5).-4(x+7)=-16<BR>\n" );
document.write( "6).5(x+3)=7(x-5)<BR>\n" );
document.write( "If youcould show the work on these, I might understand a lot better how to do it. Thank you.\r<BR>\n" );
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document.write( "Algebra is a scale.  The goal is isolate the variable.  Whatever you do to one side, do to the other side.  \r<BR>\n" );
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document.write( "1.  2x + 4 = 28   \r<BR>\n" );
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document.write( "First isolate the term containing x (2x)  so subtract 4 from both sides.\r<BR>\n" );
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document.write( "2x + 4 - 4 = 28 - 4 -->  2x = 24   \r<BR>\n" );
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document.write( "Now isolate x.  Since it is multiplied by 2, divide by 2 so x is isolated.  \r<BR>\n" );
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document.write( "(2x)/2 = 24/2 --> x = 12\r<BR>\n" );
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document.write( "17x - 42 = -39  Add 42 to both sides.  17x -42 +42 = -39 +42 -->  17x = 3\r<BR>\n" );
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document.write( "Divide both sides by 17.\r<BR>\n" );
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document.write( "(17x)/17 = 3/17  --> x=3/17\r<BR>\n" );
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document.write( "7x-2=5x+10 Get x terms on one side, so subtract 5x from both sides\r<BR>\n" );
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document.write( "7x-2-5x=5x-5x+10 --> 2x-2=10  Add 2 to both sides.\r<BR>\n" );
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document.write( "2x=12   divide both sides by 2\r<BR>\n" );
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document.write( "x=6\r<BR>\n" );
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document.write( "3x-1-x=3x+5  combine all the terms on each side (3x - x = 2x)\r<BR>\n" );
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document.write( "2x-1=3x+5  get the x's on one side, so subtract 3x from both sides\r<BR>\n" );
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document.write( "2x-3x-1=3x-3x+5 --> -x-1=5  add 1 to both sides  -x-1+1=5+1 --> -x=6\r<BR>\n" );
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document.write( "Divide both sides by -1 (so we have x instead of -x)\r<BR>\n" );
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document.write( "-x/-1 = 6/-1 -->  x=-6\r<BR>\n" );
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document.write( "-4(x+7)=-16  multiply -4 by each term inside the () (distribute it):\r<BR>\n" );
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document.write( "-4*x + -4*7 = -16 -->  -4x -28 =-16  add 28 to both sides\r<BR>\n" );
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document.write( "-4x-28+28=-16+28 --> -4x=12  divide both sides by -4\r<BR>\n" );
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document.write( "(-4x)/-4 = 12/-4  --> x = -3\r<BR>\n" );
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document.write( ".5(x+3)=7(x-5)  Distribute the numbers (multiply them by each term in the ())\r<BR>\n" );
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document.write( ".5*x +.5*3 = 7*x - 7*5 --> .5x+1.5=7x-35  subtract 7x from both sides, subtract 1.5 from both sides.\r<BR>\n" );
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document.write( ".5x + 1.5 - 1.5 -7x = 7x - 7x - 1.5 -35 -->  -6.5x = -36.5  divide both sides by -6.5\r<BR>\n" );
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document.write( "(-6.5x)/-6.5 = -36.5/-6.5 -->  x = 5.6153846...  \r<BR>\n" );
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document.write( "x is approximately 5.6\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351131 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=351131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear.solver>Linear System solver (using determinant)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Ax+%2B+a%5B12%5D%2Ay+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ax+%2B+a%5B22%5D%2Ay+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++x+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++y+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++x+=+%282%2A-1+-+0%2A1%29%2F%281%2A-1-1%2A1%29+=+1%2C%0D%0A++++++y+=+%281%2A0+-+1%2A2%29%2F%281%2A-1-1%2A1%29+=+1%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (x=1, y=1}<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "</TD></TR></TABLE>\n" );