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4.6w+0.19=55.39
We move all terms to the left:
4.6w+0.19-(55.39)=0
We add all the numbers together, and all the variables
4.6w-55.2=0
We move all terms containing w to the left, all other terms to the right
4.6w=55.2
w=55.2/4.6
w=12+7.105427357601E-15/4.6
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