From Förberedande kurs i matematik 1

Revision as of 14:21, 16 September 2008 (edit) Ian (Talk | contribs) ← Previous diff		Current revision (13:19, 23 September 2008) (edit) (undo) Tek (Talk | contribs) m
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-	Because there is an	+	Because there is an ''x'' on both the left- and right-hand sides, the first step is to subtract ''x''/3 from both sides,
-	<math>x</math>	+
-	on both the left- and right-hand sides,	+
-	the first step is to subtract	+	{{Displayed math||<math>\tfrac{1}{3}x-1-\tfrac{1}{3}x=x-\tfrac{1}{3}x</math>}}
-	<math>{x}/{3}\;</math>	+
-	from both sides,	+
		+	so as to collect ''x'' on the right-hand side
-	<math>\frac{1}{3}x-1-\frac{1}{3}x=x-\frac{1}{3}x</math>	+	{{Displayed math||<math>-1=\tfrac{2}{3}x\,\textrm{.}</math>}}
		+	Then, multiply both sides by 3/2,
-	so as to collect	+	{{Displayed math||<math>\tfrac{3}{2}\cdot (-1) = \tfrac{3}{2}\cdot\tfrac{2}{3}x\,,</math>}}
-	<math>x</math>	+
-	on the right-hand side	+
		+	so that 2/3 can be eliminated on the right-hand side to give us
-	<math>-1=\frac{2}{3}x.</math>	+	{{Displayed math||<math>-\tfrac{3}{2}=x\,\textrm{.}</math>}}
-		+
-		+
-	Then, multiply both sides by	+
-	<math>{3}/{2}\;</math>,	+
-		+
-		+
-	<math>\frac{3}{2}\centerdot \left( -1 \right)=\frac{3}{2}\centerdot \frac{2}{3}x</math>	+
-		+
-		+
-	so that	+
-	<math>{2}/{3}\;</math>	+
-	can be eliminated on the right-hand side to give us	+
-		+
-		+
-	<math>-\frac{3}{2}=x</math>	+

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Current revision

Because there is an x on both the left- and right-hand sides, the first step is to subtract x/3 from both sides,

\displaystyle \tfrac{1}{3}x-1-\tfrac{1}{3}x=x-\tfrac{1}{3}x

so as to collect x on the right-hand side

\displaystyle -1=\tfrac{2}{3}x\,\textrm{.}

Then, multiply both sides by 3/2,

\displaystyle \tfrac{3}{2}\cdot (-1) = \tfrac{3}{2}\cdot\tfrac{2}{3}x\,,

so that 2/3 can be eliminated on the right-hand side to give us

\displaystyle -\tfrac{3}{2}=x\,\textrm{.}