<s>[INST] Tips for solving linear equations Is there an easier way to solve linear equations than trial and error?
$$2(3b -1) - (4b -6) = 3$$
 [/INST] To solve $2(3b - 1) -(4b -6) =3$ for the unknown $ b $, it is best to simplify the equation's left side. To do that:


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*Distribute: $2(3b - 1) -(4b -6) = (2 \cdot 3b - 2 \cdot 1) - 1 \cdot 4b - 1 \cdot {-6} = 6b - 2 - 4b + 6$


*Combine like terms: $ 6b - 2 - 4b + 6 = 6b - 4b - 2 + 6 = 2b + 4 $
Thus, $$ 2(3b - 1) -(4b -6) =3 $$ $$ <=> 2b + 4 = 3$$
Subtract $4$ from each side of the equation:
$$ 2b + 4 - 4 = 3 - 4$$ $$<=>2b = -1$$
Finally divide $2$ to each side to isolate the unknown $b$:
$$\frac{2b}{2} = \frac{-1}{2}$$ $$<=>b = -\frac{1}{2}$$
Thus, $ b = -\frac{1}{2} $.
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