Is the equation
\(\sin(x) - 2x + y + 3 = \sin(x) - 4x\) over the real numbers
equivalent to a linear equation?
The answer is “Yes”.
First, note that the sine function is defined over all the real numbers.
Adding \(-\sin(x) + 4x - 3\) to both sides of the equation gives
\(2x + y= -3\), which fits the definition of a linear equation.