document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206626>Question 206626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I just wanted to make sure that I solved these correctly\r<BR>\n" );
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document.write( "5/8X + 1/16X= 5/16 + X   The solution is X= 1/32\r<BR>\n" );
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document.write( "also,\r<BR>\n" );
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document.write( "Use the distributive property to help you solve the equation\r<BR>\n" );
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document.write( "3(w-5)=6  W=___  ( I came up with W= 7) \r<BR>\n" );
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document.write( "Solve using the multiplication principle. \r<BR>\n" );
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document.write( "11X = -99  the solutionis X=-9  (Is this correct)\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156171 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=156171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PROBLEM 1<BR>\n" );
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document.write( "5/8X + 1/16X= 5/16 + X   The solution is X= 1/32<BR>\n" );
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document.write( "if i understand the problem correctly, your equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x ALIGN=MIDDLE  ALT=\"5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "i could not verify your answer as correct.<BR>\n" );
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document.write( "i would have solved as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x ALIGN=MIDDLE  ALT=\"5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides of the equation by 16x to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2B+1+=+5x+%2B+16x%5E2 ALIGN=MIDDLE  ALT=\"10+%2B+1+=+5x+%2B+16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+=+5x+%2B+16x%5E2 ALIGN=MIDDLE  ALT=\"11+=+5x+%2B+16x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+%2B+5x+-+11+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2+%2B+5x+-+11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "i used the quadratic formula to get a solution of:<BR>\n" );
document.write( "x = -1 or x = .6875<BR>\n" );
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document.write( "substituting in the original equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x ALIGN=MIDDLE  ALT=\"5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > should confirm the answer as correct.<BR>\n" );
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document.write( "if we let x = -1, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x ALIGN=MIDDLE  ALT=\"5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%288%2A%28-1%29%29+%2B+1%2F%2816%2A%28-1%29%29+=+5%2F16+%2B+%28-1%29 ALIGN=MIDDLE  ALT=\"5%2F%288%2A%28-1%29%29+%2B+1%2F%2816%2A%28-1%29%29+=+5%2F16+%2B+%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This becomes -(5/8) - (1/16) = (5/16) - 1<BR>\n" );
document.write( "which becomes -11/16 = -11/16 confirming x = -1 is correct.<BR>\n" );
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document.write( "if we let x = .6875, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x ALIGN=MIDDLE  ALT=\"5%2F%288x%29+%2B+1%2F%2816x%29+=+5%2F16+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%285.5%29+%2B+1%2F%2811%29+=+5%2F16+%2B+.6875 ALIGN=MIDDLE  ALT=\"5%2F%285.5%29+%2B+1%2F%2811%29+=+5%2F16+%2B+.6875\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This becomes .90909090909... + .0909090909091... = .3125 + .6875<BR>\n" );
document.write( "which becomes 1 = 1 confirming x = .6875 is also correct.<BR>\n" );
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document.write( "a graph of this equation would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-100%2C100%2C16x%5E2%2B5x-11%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-100%2C100%2C16x%5E2%2B5x-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "an alternative interpretation of this problem would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F8%29%2Ax+%2B+%281%2F16%29%2Ax+=+5%2F16+%2B+x ALIGN=MIDDLE  ALT=\"%285%2F8%29%2Ax+%2B+%281%2F16%29%2Ax+=+5%2F16+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "i would have solved as follows:<BR>\n" );
document.write( "multiply both sides of this equation by 16 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x+%2B+x+=+5+%2B+16x ALIGN=MIDDLE  ALT=\"10x+%2B+x+=+5+%2B+16x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:<BR>\n" );
document.write( "11x = 5 + 16x<BR>\n" );
document.write( "subtract 11x from both sides and subtract 5 from both sides to get:<BR>\n" );
document.write( "5x = -5<BR>\n" );
document.write( "divide both sides by 5 to get:<BR>\n" );
document.write( "x = -1<BR>\n" );
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document.write( "substitute in the original equation of 11x = 5 + 16x gets -11 = -11 confirming the answer is correct.<BR>\n" );
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document.write( "PROBLEM 2<BR>\n" );
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document.write( "3(w-5)=6  W=___  ( I came up with W= 7) <BR>\n" );
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document.write( "this looks good.<BR>\n" );
document.write( "substituting in your original equation we get:<BR>\n" );
document.write( "3*(7-5) = 6<BR>\n" );
document.write( "which becomes 3*2 = 6 which becomes 6 = 6 which means w = 7 is good.<BR>\n" );
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document.write( "PROBLEM 3<BR>\n" );
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document.write( "11X = -99  the solution is X=-9  (Is this correct)<BR>\n" );
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document.write( "this also looks good.<BR>\n" );
document.write( "substituting in your original equation we get:<BR>\n" );
document.write( "11*(-9) = -99 which becomes -99 = -99 which means x = -9 is good.<BR>\n" );
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document.write( " </SPAN>\n" );
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