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Lösung 2.2:2b

(Unterschied zwischen Versionen)

Version vom 13:54, 22. Okt. 2008

First, we multiply both sides in the equation by 47=28, so that we get rid of the denominators in the equation,

78x+3−

45x−7=4

(8x+3)−7

(5x−7)=56.

We can simplify the left-hand side to 4(8x+3)−7(5x−7)=32x+12−35x+49=−3x+61. Hence, the equation is

−3x+61=56.

We solve this equation by subtracting 61 from both sides and then dividing by -3,

−3x+61−61−3x−3−3xx=56−61

=−5

=−3−5

=35.

The answer is x=53.

As the final part of the solution, check the answer by substituting x=53 into the original equation

LHS=78

35+3−45

35−7=7

35+3

3−4

35−7

3=7

5+3

3−4

5−7

3=2140+9−1225−21=2149−412=3

7−2

3=37−31=37−1=36=2=RHS.