$$ \begin{aligned} -91 &= 7\cdot(1+7k)&& \text{simplify right side} \\[1 em]-91 &= 7+49k&& \\[1 em]-91 &= 49k+7&& \text{ swap the left and right side of the equation } \\[1 em]49k+7 &= -91&& \text{ move 7 to the right } \\[1 em]49k &= -91-7&& \\[1 em]49k &= -98&& \text{ divide both sides by $ 49 $ } \\[1 em]k &= -\frac{98}{49}&& \\[1 em]k &= -2&& \\[1 em] \end{aligned} $$

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