Solution 2.2:2b - Revision history

Tek at 14:05, 23 September 2008

Tek — Tue, 23 Sep 2008 14:05:03 GMT

←Older revision		Revision as of 14:05, 23 September 2008
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-	First, we multiply both sides in the equation by	+	First, we multiply both sides in the equation by <math>4\cdot 7=28</math>, so that we get rid of the denominators in the equation,
-	<math>4\~~centerdot~~ 7=28</math>, so that we get rid of the denominators in the equation,	+

		+	{{Displayed math\|\|<math>\begin{align}
		+	& 4\cdot{}\rlap{/}7\cdot\frac{8x+3}{\rlap{/}7} - \rlap{/}4\cdot 7\cdot\frac{5x-7}{\rlap{/}4} = 4\cdot 7\cdot 2\\[5pt]
		+	&\qquad\Leftrightarrow\quad 4\cdot (8x+3) - 7\cdot (5x-7) = 56\,\textrm{.}
		+	\end{align}</math>}}

-	<math>~~\begin{align}~~	+	We can simplify the left-hand side to <math>4\cdot (8x+3) - 7\cdot (5x-7) = 32x+12-35x+49 = -3x+61\,</math>. Hence, the equation is
-	& 4\~~centerdot 7\centerdot \frac{8x+3}{7}-4\centerdot 7\centerdot \frac{5x-7}{4}=4\centerdot 7\centerdot 2 \\~~	+
-	~~& \Leftrightarrow 4\centerdot \left~~( 8x+3 ~~\right~~)-7\~~centerdot \left~~( 5x-7 ~~\right~~)=~~56 \\~~	+
-	\~~end{align}~~</math>	+

		+	{{Displayed math\|\|<math>-3x+61=56\,\textrm{.}</math>}}

-	We ~~can simplify the left~~-~~hand side to~~ ,	+	We solve this equation by subtracting 61 from both sides and then dividing by -3,

		+	{{Displayed math\|\|<math>\begin{align}
		+	-3x+61-61&=56-61\,,\\[5pt]
		+	-3x&=-5\,,\\[5pt]
		+	\frac{-3x}{-3}&=\frac{-5}{-3}\,,\\[5pt]
		+	x&=\frac{5}{3}\,\textrm{.}
		+	\end{align}</math>}}

-	<math>~~4\centerdot \left( 8x+~~3 \~~right)-7\centerdot \left( 5x-7 \right)=32x+12-35x+49=-3x+61~~</math>	+	The answer is <math>x={5}/{3}\,</math>.

		+	As the final part of the solution, check the answer by substituting <math>x={5}/{3}</math> into the original equation

-	~~Hence, the equation is~~	+	{{Displayed math\|\|<math>\begin{align}
-		+	\text{LHS}
-		+	&= \frac{8\cdot\frac{5}{3}+3}{7}-\frac{5\cdot\frac{5}{3}-7}{4}
-	~~<math>-3x+61=56</math>~~	+	= \frac{\bigl(8\cdot\frac{5}{3}+3\bigr)\cdot 3}{7\cdot 3} - \frac{\bigl( 5\cdot \frac{5}{3}-7\bigr)\cdot 3}{4\cdot 3}\\[5pt]
-		+	&= \frac{8\cdot 5+3\cdot 3}{7\cdot 3}-\frac{5\cdot 5-7\cdot 3}{4\cdot 3}
-		+	= \frac{40+9}{21}-\frac{25-21}{12}\\[5pt]
-	~~We solve this equation by subtracting~~	+	&= \frac{49}{21}-\frac{4}{12}
-	~~<math>61</math>~~	+	= \frac{7\cdot 7}{3\cdot 7} - \frac{2\cdot 2}{2\cdot 2\cdot 3}
-	~~from both sides and then dividing by~~	+	= \frac{7}{3}-\frac{1}{3}
-	~~<math>-3</math>,~~	+	= \frac{7-1}{3}
-		+	= \frac{6}{3} = 2 = \text{RHS.}
-		+	\end{align}</math>}}
-	~~<math>\begin~~{~~align}~~	+
-	~~& -3x+61-61=56-61 \\~~	+
-	~~& -3x=-5 \\~~	+
-	~~& \frac~~{~~-3x}{-3}=\frac{-5}{-3} \\~~	+
-	~~& x=\frac{5}{3} \\~~	+
-	~~\end{align}</~~math>	+
-		+
-		+
-	~~The answer is~~	+
-	~~<math>x={5}/{3}\;</math>.~~	+
-		+
-	~~As the final part of the solution, check the answer by substituting~~	+
-	~~<math>x={5}/{3}\;</math>~~	+
-	~~into the original equation~~	+
-		+
-		+
-	<math>\begin{align}	+
-	& \text{LHS}~~\quad~~ =~~\quad~~ \frac{8\~~centerdot~~ \frac{5}{3}+3}{7}-\frac{5\~~centerdot~~ \frac{5}{3}-7}{4}=\frac{\~~left~~( 8\~~centerdot~~ \frac{5}{3}+3 \~~right~~)\~~centerdot~~ 3}{7\~~centerdot~~ 3}-\frac{\~~left~~( 5\~~centerdot~~ \frac{5}{3}-7 \~~right~~)\~~centerdot~~ 3}{4\~~centerdot~~ 3} \\	+
-	~~& \\~~	+
-	& =\frac{8\~~centerdot~~ 5+3\~~centerdot~~ 3}{7\~~centerdot~~ 3}-\frac{5\~~centerdot~~ 5-7\~~centerdot~~ 3}{4\~~centerdot~~ 3}=\frac{40+9}{21}-\frac{25-21}{12} \\	+
-	~~& \\~~	+
-	& =\frac{49}{21}-\frac{4}{12}=\frac{7\~~centerdot~~ 7}{3\~~centerdot~~ 7}-\frac{2\~~centerdot~~ 2}{2\~~centerdot~~ 2\~~centerdot 2~~}=\frac{7}{3}-\frac{1}{3}=\frac{7-1}{3} \\	+
-	~~& \\~~	+
-	& =\frac{6}{3}=2~~\quad~~ =~~\quad~~ \text{RHS} \\	+
-	\end{align}</math>	+

Ian at 12:45, 17 September 2008

Ian — Wed, 17 Sep 2008 12:45:39 GMT

←Older revision		Revision as of 12:45, 17 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	First, we multiply both sides in the equation by
-	<~~center~~> ~~[[Image:2_2_2b~~-1(2)~~.gif]]~~ </~~center~~>	+	<math>4\centerdot 7=28</math>, so that we get rid of the denominators in the equation,
-	{{~~NAVCONTENT_STOP~~}}	+
-	{{~~NAVCONTENT_START~~}}	+
-	<~~center~~> ~~[[Image:2_2_2b-2(2)~~.~~gif]]~~ </~~center~~>	+	<math>\begin{align}
-	{{~~NAVCONTENT_STOP~~}}	+	& 4\centerdot 7\centerdot \frac{8x+3}{7}-4\centerdot 7\centerdot \frac{5x-7}{4}=4\centerdot 7\centerdot 2 \\
		+	& \Leftrightarrow 4\centerdot \left( 8x+3 \right)-7\centerdot \left( 5x-7 \right)=56 \\
		+	\end{align}</math>
		+
		+
		+	We can simplify the left-hand side to ,
		+
		+
		+	<math>4\centerdot \left( 8x+3 \right)-7\centerdot \left( 5x-7 \right)=32x+12-35x+49=-3x+61</math>
		+
		+
		+	Hence, the equation is
		+
		+
		+	<math>-3x+61=56</math>
		+
		+
		+	We solve this equation by subtracting
		+	<math>61</math>
		+	from both sides and then dividing by
		+	<math>-3</math>,
		+
		+
		+	<math>\begin{align}
		+	& -3x+61-61=56-61 \\
		+	& -3x=-5 \\
		+	& \frac{-3x}{-3}=\frac{-5}{-3} \\
		+	& x=\frac{5}{3} \\
		+	\end{align}</math>
		+
		+
		+	The answer is
		+	<math>x={5}/{3}\;</math>.
		+
		+	As the final part of the solution, check the answer by substituting
		+	<math>x={5}/{3}\;</math>
		+	into the original equation
		+
		+
		+	<math>\begin{align}
		+	& \text{LHS}\quad =\quad \frac{8\centerdot \frac{5}{3}+3}{7}-\frac{5\centerdot \frac{5}{3}-7}{4}=\frac{\left( 8\centerdot \frac{5}{3}+3 \right)\centerdot 3}{7\centerdot 3}-\frac{\left( 5\centerdot \frac{5}{3}-7 \right)\centerdot 3}{4\centerdot 3} \\
		+	& \\
		+	& =\frac{8\centerdot 5+3\centerdot 3}{7\centerdot 3}-\frac{5\centerdot 5-7\centerdot 3}{4\centerdot 3}=\frac{40+9}{21}-\frac{25-21}{12} \\
		+	& \\
		+	& =\frac{49}{21}-\frac{4}{12}=\frac{7\centerdot 7}{3\centerdot 7}-\frac{2\centerdot 2}{2\centerdot 2\centerdot 2}=\frac{7}{3}-\frac{1}{3}=\frac{7-1}{3} \\
		+	& \\
		+	& =\frac{6}{3}=2\quad =\quad \text{RHS} \\
		+	\end{align}</math>

Tekbot: Lösning 2.2:2b moved to Solution 2.2:2b: Robot: moved page

Tekbot — Tue, 09 Sep 2008 08:44:03 GMT

Lösning 2.2:2b moved to Solution 2.2:2b: Robot: moved page

←Older revision

Revision as of 08:44, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 06:39:09 GMT

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

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Lina — Mon, 31 Mar 2008 14:30:04 GMT

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