document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196758>Question 1196758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I can list all of the properties I need for this big test, but I don't know how to apply my knowledge:( can you explain what I need to do for the following---<BR>\n" );
document.write( "division property of equality<BR>\n" );
document.write( "subtraction property of equality<BR>\n" );
document.write( "addition property of equality<BR>\n" );
document.write( "substitution property of equality<BR>\n" );
document.write( "reflexive property<BR>\n" );
document.write( "symmetric property<BR>\n" );
document.write( "transitive property<BR>\n" );
document.write( "Please and 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 #829748 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The ones that have \"of equality\" apply to equations. With exception to substitution, we're doing the same thing to both sides of an equation.\r<BR>\n" );
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document.write( "The division property of equality has us divide both sides by the same number.<BR>\n" );
document.write( "The rule is if a = b, then a/c = b/c where c is not zero.<BR>\n" );
document.write( "We need c nonzero to avoid division by zero errors.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "2x = 10<BR>\n" );
document.write( "2x/2 = 10/2<BR>\n" );
document.write( "x = 5<BR>\n" );
document.write( "I divided both sides by 2\r<BR>\n" );
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document.write( "The subtraction property of equality is where we subtract the same thing from both sides<BR>\n" );
document.write( "The rule is if a = b, then a-c = b-c<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "x+1 = 7<BR>\n" );
document.write( "x+1-1 = 7-1<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "We subtract 1 from both sides to undo the +1\r<BR>\n" );
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document.write( "The additional property of equality is going to follow the same idea, but this time we add the same thing to both sides<BR>\n" );
document.write( "If a = b, then a+c = b+c<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "w-12 = 20<BR>\n" );
document.write( "w-12+12 = 20+12<BR>\n" );
document.write( "w = 32<BR>\n" );
document.write( "Add 12 to both sides to undo the subtraction applied to w\r<BR>\n" );
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document.write( "Not mentioned, but should be, is the multiplicative property of equality<BR>\n" );
document.write( "If a = b, then a*c = b*c<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "x/3 = 18<BR>\n" );
document.write( "3*(x/3) = 3*18 ... multiply both sides by 3<BR>\n" );
document.write( "x = 54\r<BR>\n" );
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document.write( "The substitution property of equality is where we replace a variable with its stated value (if given or known)<BR>\n" );
document.write( "For instance, if we know that x = 54, then x/3 = 18 becomes 54/3 = 18. <BR>\n" );
document.write( "Recall that variables are simply placeholders for numbers, so it makes sense to swap out the letters for actual numbers.<BR>\n" );
document.write( "Think of the variable as a box that holds the number.\r<BR>\n" );
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document.write( "Sometimes we may replace one variable with another algebraic expression<BR>\n" );
document.write( "Example: if x = y+10, then 2x+3y = 10 becomes 2(y+10)+3y = 10. I replaced x with (y+10).\r<BR>\n" );
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document.write( "It might help to think of a substitute teacher in that they temporarily replace your current teacher. That's one way to remember how the substitution property works.\r<BR>\n" );
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document.write( "Now to the other properties.\r<BR>\n" );
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document.write( "The reflexive property is the idea of x = x. Any value is equal to itself. This may seem trivial, but it's useful for proofs later down the road.\r<BR>\n" );
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document.write( "The symmetric property is the idea of y = x being the same as x = y. We can swap both sides of any equation. The order of left vs right doesn't matter<BR>\n" );
document.write( "Example: 2+3 = 5 is the same as 5 = 2+3<BR>\n" );
document.write( "It's up to preference which you think is the better format. Sometimes one format is more convenient than others.\r<BR>\n" );
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document.write( "Transitive property:<BR>\n" );
document.write( "If a = b and b = c, then a = c<BR>\n" );
document.write( "I like to think of this as a bunch of dominoes.<BR>\n" );
document.write( "If A knocks down B, and B knocks over C, then A caused C to fall\r<BR>\n" );
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document.write( "We can think of the transitive property as a very close cousin of the substitution property<BR>\n" );
document.write( "If a = b and b = c, then we can replace 'b' in the first equation with 'c'<BR>\n" );
document.write( "So we go from a = b to a = c\r<BR>\n" );
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document.write( "These terms may seem like a lot to memorize. So I recommend using flashcards. Or you can just practice solving equations. When solving equations, be sure to list the property used. Refer to these set of steps as an example<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Equation</TD><TD >Reason</TD><TD >Further Clarification</TD></tr><tr><TD >3x+5 = 10</TD><TD ></TD><TD ></TD></tr><tr><TD >3x+5-5 = 10-5</TD><TD >Subtraction Property of Equality</TD><TD >Subtract 5 from both sides</TD></tr><tr><TD >3x = 5</TD><TD >Simplify</TD><TD ></TD></tr><tr><TD >3x/3 = 5/3</TD><TD >Division Property of Equality</TD><TD >Divide both sides by 3</TD></tr><tr><TD >x = 5/3</TD><TD >Simplify</TD><TD ></TD></tr>\n" );
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document.write( "Another example<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Equation</TD><TD >Reason</TD><TD >Further Clarification</TD></tr><tr><TD >(x/5) - 2 = 12</TD><TD ></TD><TD ></TD></tr><tr><TD >(x/5) - 2+2 = 12+2</TD><TD >Addition Property of Equality</TD><TD >Add 2 to both sides</TD></tr><tr><TD >x/5 = 14</TD><TD >Simplify</TD><TD ></TD></tr><tr><TD >5*(x/5) = 5*14</TD><TD >Multiplication Property of Equality</TD><TD >Multiply both sides by 5</TD></tr><tr><TD >x = 70</TD><TD >Simplify</TD><TD ></TD></tr>\n" );
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document.write( "How can we check the answer to an equation? By the substitution property.<BR>\n" );
document.write( "Let's replace each x in the second example with 70. Then simplify by use of the order of operations (PEMDAS)<BR>\n" );
document.write( "(x/5) - 2 = 12<BR>\n" );
document.write( "(70/5) - 2 = 12<BR>\n" );
document.write( "14 - 2 = 12<BR>\n" );
document.write( "12 = 12<BR>\n" );
document.write( "We get the same thing on both sides which confirms x = 70 is indeed the solution to that equation.\r<BR>\n" );
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document.write( "Side note: When solving equations, we go in reverse of PEMDAS to undo each operation done to the variable we're solving for.<BR>\n" );
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