Solution 2.3:3e - Revision history

Tek at 08:47, 29 September 2008

2008-09-29T08:47:48Z

←Older revision		Revision as of 08:47, 29 September 2008
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-	In this case, we see that the left-hand side contains the factor	+	In this case, we see that the left-hand side contains the factor <math>x+3</math>, which we can take out to obtain
-	<math>x+~~\text{~~3}</math>, which we can take out to obtain	+
-		+
-		+
-	~~<math>\begin{align}~~	+
-	~~& \left( x+\text{3} \right)\left( x-1 \right)-\left( x+\text{3} \right)\left( 2x-9 \right)=\left( x+\text{3} \right)\left( \left( x-1 \right)-\left( 2x-9 \right) \right) \\~~	+
-	~~& =\left( x+\text{3} \right)\left( x-1-2x+9 \right)=\left( x+\text{3} \right)\left( -x+8 \right). \\~~	+
-	~~\end{align}</math>~~	+

		+	{{Displayed math\|\|<math>\begin{align}
		+	(x+3)(x-1) - (x+3)(2x-9)
		+	&= (x+3)\bigl((x-1)-(2x-9)\bigr)\\[5pt]
		+	&= (x+3)(x-1-2x+9)\\[5pt]
		+	&= (x+3)(-x+8)\,\textrm{.}
		+	\end{align}</math>}}

	This rewriting of the equation results in the new equation		This rewriting of the equation results in the new equation

		+	{{Displayed math\|\|<math>(x+3)(-x+8)=0</math>}}

-	~~<math>\left( x+\text{3} \right)\left( -x+8 \right)=0</math>~~	+	which has the solutions <math>x=-3</math> and <math>x=8\,</math>.
-		+
-		+
-	which has the solutions	+
-	<math>x=-~~\text{~~3}</math>	+
-	and	+
-	<math>x=~~\text{~~8}</math>.	+

-	We check the solution	+	We check the solution <math>x=8</math> by substituting it into the equation,
-	<math>x=~~\text{~~8 }</math>	+
-	by substituting it into the equation:	+

-	~~LHS~~	+	{{Displayed math\|\|<math>\text{LHS} = (8+3)\cdot (8-1) - (8+3)\cdot (2\cdot 8 - 9) = 11\cdot 7 - 11\cdot 7 = 0 = \textrm{RHS.}</math>}}
-	<math>=~~\left~~( 8+3 ~~\right~~)\~~centerdot \left~~( 8-1 ~~\right~~)-~~\left~~( 8+3 ~~\right~~)\~~centerdot \left~~( 2\~~centerdot~~ 8-9 ~~\right~~)=11\~~centerdot~~ 7-11\~~centerdot~~ 7=0=</math>	+
-	~~RHS~~	+

Ian at 15:14, 20 September 2008

2008-09-20T15:14:45Z

←Older revision		Revision as of 15:14, 20 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	In this case, we see that the left-hand side contains the factor
-	<~~center~~> ~~[[Image:2_3_3e.gif]]~~ </~~center~~>	+	<math>x+\text{3}</math>, which we can take out to obtain
-	{{~~NAVCONTENT_STOP~~}}	+
		+
		+	<math>\begin{align}
		+	& \left( x+\text{3} \right)\left( x-1 \right)-\left( x+\text{3} \right)\left( 2x-9 \right)=\left( x+\text{3} \right)\left( \left( x-1 \right)-\left( 2x-9 \right) \right) \\
		+	& =\left( x+\text{3} \right)\left( x-1-2x+9 \right)=\left( x+\text{3} \right)\left( -x+8 \right). \\
		+	\end{align}</math>
		+
		+
		+	This rewriting of the equation results in the new equation
		+
		+
		+	<math>\left( x+\text{3} \right)\left( -x+8 \right)=0</math>
		+
		+
		+	which has the solutions
		+	<math>x=-\text{3}</math>
		+	and
		+	<math>x=\text{8}</math>.
		+
		+	We check the solution
		+	<math>x=\text{8 }</math>
		+	by substituting it into the equation:
		+
		+	LHS
		+	<math>=\left( 8+3 \right)\centerdot \left( 8-1 \right)-\left( 8+3 \right)\centerdot \left( 2\centerdot 8-9 \right)=11\centerdot 7-11\centerdot 7=0=</math>
		+	RHS

Tekbot: Lösning 2.3:3e moved to Solution 2.3:3e: Robot: moved page

2008-09-09T08:59:23Z

Lösning 2.3:3e moved to Solution 2.3:3e: Robot: moved page

←Older revision

Revision as of 08:59, 9 September 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-21T06:46:49Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

←Older revision		Revision as of 06:46, 21 August 2008
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2008-04-01T10:03:57Z

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