document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163505>Question 163505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equations.\r<BR>\n" );
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document.write( "1) 2x = 7x + 2<BR>\n" );
document.write( "2x - 7x = 7x - 7x + 2<BR>\n" );
document.write( "-5x = 2<BR>\n" );
document.write( "x = -2/5\r<BR>\n" );
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document.write( "2) y/5 = 4<BR>\n" );
document.write( "y/5 * 5 = 4 * 5 (Multiply both sides by 5)<BR>\n" );
document.write( "y = 20\r<BR>\n" );
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document.write( "3) x/2 - 3 = 4<BR>\n" );
document.write( "x/2 - 3 + 3 = 4 + 3<BR>\n" );
document.write( "x/2 = 7 (Multiply both sides by 2)<BR>\n" );
document.write( "x = 14\r<BR>\n" );
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document.write( "4.  OH NUTS! SELLS CASHEWS FOR $6.75 PER POUND AND BRAZIL NUTS FOR $5.00 PER POUND.  HOW MUCH OF EACH TYPE SHOULD BE USED TO MAKE A 50lb MIXTURE THAT SELLS FOR $5.70 PER POUND?\r<BR>\n" );
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document.write( "5. Try 5x - 7y = 35\r<BR>\n" );
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document.write( "What are the x and y intercepts? Graph your answer use any method of your choice to solve.<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 #120484 by </B><A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><B>KnightOwlTutor(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><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=KnightOwlTutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first three problems are correct.\r<BR>\n" );
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document.write( "4. x=# of pounds of cashews<BR>\n" );
document.write( "50-x=# of pounds of brazil nuts.\r<BR>\n" );
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document.write( "5(50-x)+6.75x=5.70(50)\r<BR>\n" );
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document.write( "250-5x+6.75x=285\r<BR>\n" );
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document.write( "add the x terms to simplify\r<BR>\n" );
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document.write( "250+1.75x=285\r<BR>\n" );
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document.write( "Subtract 250 from both sides\r<BR>\n" );
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document.write( "1.75x=35\r<BR>\n" );
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document.write( "Divide both sides by 75\r<BR>\n" );
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document.write( "x=20\r<BR>\n" );
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document.write( "Let's check our answer<BR>\n" );
document.write( "5(30)+6.75(20)=285\r<BR>\n" );
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document.write( "150+135=285\r<BR>\n" );
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document.write( "5x - 7y = 35<BR>\n" );
document.write( "Subtract 5x from both sides\r<BR>\n" );
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document.write( "-7y=35-5x\r<BR>\n" );
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document.write( "Divide both sides by -7\r<BR>\n" );
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document.write( "y=-5+(5/7)x<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=describe_linear_equation.solver>DESCRIBE a linear EQUATION: slope, intercepts, etc</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+x+%2B+-7+y+=+35 ALIGN=MIDDLE  ALT=\"5+x+%2B+-7+y+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" > describes a sloping line. For any <BR>\n" );
document.write( "  equation ax+by+c = 0, slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Fb+=+-5%2F-7 ALIGN=MIDDLE  ALT=\"-a%2Fb+=+-5%2F-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<UL><LI>X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x =  c/a. 35/5 = 7.</LI><LI>Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 35/-7 = -5.</LI><LI>Slope is -5/-7 = 0.714285714285714.</LI><LI> Equation in slope-intercept form: y=0.714285714285714*x+-5.</LI></UL><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+7-8%2C+7%2B8%2C+-5-8%2C+-5%2B8%2C+0.714285714285714%2Ax%2B-5+%29+ ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+7-8%2C+7%2B8%2C+-5-8%2C+-5%2B8%2C+0.714285714285714%2Ax%2B-5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\n" );
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document.write( "the y intercept is (0,-5)<BR>\n" );
document.write( "The x intercept is  (0,7)\r<BR>\n" );
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