document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116727>Question 116727</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/013052316X/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 17 -(4k - 2) > 2 (k + 3)   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84874 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=84874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can work these problems pretty much following the same rules as you would for solving an<BR>\n" );
document.write( "equation. The inequality sign is similar to the equal sign in the equation in separating<BR>\n" );
document.write( "the two sides from each other. There is an exception, however. If you multiply or divide<BR>\n" );
document.write( "both sides of the inequality by a negative quantity, you reverse the direction of the inequality<BR>\n" );
document.write( "sign.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So let's begin using the processes we would use for solving if the given problem were an equation.<BR>\n" );
document.write( "Start with the given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "17 -(4k - 2) > 2*(k + 3) <BR>\n" );
document.write( ".<BR>\n" );
document.write( "On the right side, do the distributed multiplication to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "17 -(4k - 2) > 2k + 6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "On the left side remove the parentheses. However, since the parentheses are preceded by<BR>\n" );
document.write( "a minus sign, when you remove the parentheses you change the signs of the two terms inside<BR>\n" );
document.write( "the parentheses to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "17 - 4k + 2 > 2k + 6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now, as in solving an equation, we try to collect the terms with the variable k on one side<BR>\n" );
document.write( "of the > sign and all the numerical terms on the other side. Begin by subtracting 2k<BR>\n" );
document.write( "from both sides of the inequality to get rid of the 2k on the right side. This subtraction <BR>\n" );
document.write( "reduces the inequality to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "17 - 6k + 2 > 6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "On the left side combine the 17 and the +2 to get 19:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "19 - 6k > 6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the 19 on the left side by subtracting 19 from both sides:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-6k > -13<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for k by dividing both sides by -6. However, recall the rule that if you divide both<BR>\n" );
document.write( "sides by a negative quantity, you reverse the direction of the inequality sign. So dividing<BR>\n" );
document.write( "both sides by -6 results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "k < 13/6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That is the answer to this problem. The original inequality will be true if k is less than 13/6.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's try it to help verify. If we let k = 2 (which is slightly less than 13/6) then the<BR>\n" );
document.write( "original inequality becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "17 - (8 - 2) > 2(2 + 3)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Combine the terms in the parentheses on both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "17 - (6) > 2(5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Do the math. On the left side 17 - 6 = 11 and on the right side 2*5 = 10. So when k = 2<BR>\n" );
document.write( "the inequality is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "11 > 10<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That is true. To further check the answer you might want to try letting k = 3 (which is<BR>\n" );
document.write( "not less than 13/6) and see what the original inequality becomes when k is that value.<BR>\n" );
document.write( "You should find that the resulting inequality is not true ... showing that if k is bigger than<BR>\n" );
document.write( "13/6 the inequality will not work.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand how to work problems such as these. Don't forget the<BR>\n" );
document.write( "rule about reversing the direction of the inequality sign if you multiply or divide both<BR>\n" );
document.write( "sides by a negative quantity.<BR>\n" );
document.write( ".  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );