We need to solve for k. So, let's start by isolating terms with k in them on one side of the equation and terms without k in them on the other side of the equation. We can add "dk" to both sides, and add "b" to both sides. We obtain:
ak + dk = c + b
Now, on the left side of the equation we can do some manipulation to further isolate k. We see that "ak" and "dk" have a common factor of k, so we can pull that common factor out, like so:
k(a + d) = c + b
We know that k(a + d) = ak + dk because when we distribute the k throughout the parentheses on the left side of the equation, we obtain the original expression ak + dk. Now, we can divide both sides of the equation by (a + d), completely isolating k:
And, we have found the value of k! the correct answer is (E).
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