Is there a constant by which I can multiply to invert one sign? Take the equation $A(x - 7) = x + 7$. Is this possible?
In other words, is there any constant $A$ by which $(x - 7)$ can be multiplied to become $(x + 7)$?
Notes:


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*$x$ is any real number.

*The original question was $x + 7 = A(x - 7) + B(x + 5)$. I thought I'd be clever and set $B$ to $0$, but I realized I had no idea what $A$ should be.


To solve the actual problem consider collecting everything to one side.
You will notice that overall the equation of $(x-Ax-Bx)+(7+7A-5B)=0$ must be 0 independent of choice of $x$. What does that tell you about the relationship between $A$ and $B$? You will also note the constant term must be 0, what does that tell you about $A$ and $B$? Can you relate the expressions to solve for $A$ and $B$? (2 equations, 2 unknowns)
