document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209252>Question 1209252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What value of x is in the solution set  -2(3x+2) > -8x+6<BR>\n" );
document.write( "(a) -5<BR>\n" );
document.write( "(b) 6<BR>\n" );
document.write( "(c) 5<BR>\n" );
document.write( "(d) -6 </SPAN>\n" );
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document.write( "Answer: <font color=red>6  (choice B)</font>\r<BR>\n" );
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document.write( "Work Shown<BR>\n" );
document.write( "-2(3x+2) > -8x+6<BR>\n" );
document.write( "-6x-4 > -8x+6<BR>\n" );
document.write( "-6x+8x > 6+4<BR>\n" );
document.write( "2x > 10<BR>\n" );
document.write( "x > 10/2<BR>\n" );
document.write( "x > 5<BR>\n" );
document.write( "Anything larger than 5 is in the solution set. <BR>\n" );
document.write( "Of the choices you listed, only <font color=red>x = 6</font> works as a solution.\r<BR>\n" );
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document.write( "Another approach\r<BR>\n" );
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document.write( "Since we're given a list of choices, we can plug them one at a time into the original inequality. <BR>\n" );
document.write( "If we get a true statement at the end, then we have a solution.\r<BR>\n" );
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document.write( "Let's try choice (a)<BR>\n" );
document.write( "Plug in x = -5<BR>\n" );
document.write( "-2(3x+2) > -8x+6<BR>\n" );
document.write( "-2(3*(-5)+2) > -8*(-5)+6<BR>\n" );
document.write( "-2(-15+2) > 40+6<BR>\n" );
document.write( "-2(-13) > 46<BR>\n" );
document.write( "26 > 46<BR>\n" );
document.write( "The last inequality at the end is false, so the original inequality is false when x = -5. We can rule out choice (a)\r<BR>\n" );
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document.write( "Now let's try choice (b)<BR>\n" );
document.write( "Plug in x = 6<BR>\n" );
document.write( "-2(3x+2) > -8x+6<BR>\n" );
document.write( "-2(3*6+2) > -8*6+6<BR>\n" );
document.write( "-2(18+2) > -48+6<BR>\n" );
document.write( "-2(20) > -42<BR>\n" );
document.write( "-40 > -42<BR>\n" );
document.write( "We arrive at a true claim. <BR>\n" );
document.write( "It might help to make a (vertical) number line to see that -40 is larger than -42.<BR>\n" );
document.write( "Or you can multiply both sides by -1 to go from -40 > -42 to 40 < 42. <BR>\n" );
document.write( "Don't forget to flip the inequality sign when multiplying both sides by a negative number.<BR>\n" );
document.write( "The last inequality is true, so the original inequality is true when <font color=red>x = 6</font> <BR>\n" );
document.write( "The answer is <font color=red>choice (b)</font>\r<BR>\n" );
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document.write( "You should find that x = 5 and x = -6 will make the inequality false, so we can rule out choices (c) and (d).<BR>\n" );
document.write( "I'll let the student handle the scratch work for these cases.<BR>\n" );
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