Question Completed: 11 of 20 My score: 11/20 Solve the following equation. \[ -(x-2)+5=6 x+7(1-x) \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x=2 \) (Simplify your answer.) B. The solution is all real numbers. C. There is no solution.

To solve the equation \(- (x - 2) + 5 = 6x + 7(1 - x)\), let's first simplify both sides. On the left-hand side: \(- (x - 2) + 5 = -x + 2 + 5 = -x + 7\). On the right-hand side, distribute \(7\): \(6x + 7(1 - x) = 6x + 7 - 7x = -x + 7\). Now we have: \(-x + 7 = -x + 7\). Since both sides are identical, this means that the equation holds true for all values of \(x\). So the answer is B: The solution is all real numbers. Now, here’s something you might enjoy! Who knew math could be so harmonious? Just like every good song has its recurring theme, equations like this remind us that sometimes life (and math!) can be beautifully simple. And if you're curious about exploring more equations with interesting properties, diving into linear algebra could be your next fun adventure—think transformations and vector spaces!