Dependent Voltage Source KCL question

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SUMMARY

The discussion centers on a KCL (Kirchhoff's Current Law) problem involving a dependent voltage source. The user struggles with the transition from the equation (2-v)/20 = (Vx-2Vx)/8 - (Vx-8)/4 to the simplified form 17V - 18Vx = 84. The confusion arises from the manipulation of fractions, suggesting that the solution manual likely multiplied the entire equation by a constant to eliminate the fractions. Understanding this step is crucial for solving similar KCL problems effectively.

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sdusheyko
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I'm having trouble figuring out the KCL portion of this problem.

I have no idea how in the world the solution does from;

(2-v)/20 = (Vx-2Vx)/8 - (Vx-8)/4

to;

17V - 18Vx = 84

it doesn't seem to make sense; but neither does my solution. i think I'm missing some concept here but cannot put my figure on it.

Thanks.
 

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By eyeballing it, I'd say the solutions manual probably multiplied the entire equation by some constant to make all the fractions go away.
 

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