Final answer:
All equations A) 1/2x = -50, B) -60t = 30, C) x + 90 = -100, and D) -0.01 = -0.001x are linear and can be manipulated into the standard linear form ax + b = 0, making none of them fundamentally different based solely on their linear nature.
Step-by-step explanation:
When evaluating which equation does not belong amongst A) 1/2x = -50, B) -60t = 30, C) x + 90 = -100, and D) -0.01 = -0.001x, we look for an equation that is fundamentally different from the others. Each of these equations is linear, meaning that they can be written in the form ax + b = 0, where a and b are constants. It is evident that the equations in options A, B, and C have one variable and can be easily manipulated to the standard form, while option D includes a fractional coefficient which is less straightforward.
Option A simplifies to x = -100; option B simplifies to t = -1/2; option C simplifies to x = -190. Option D, however, simplifies to x = 10. The manipulation of fractions in D might lead students to believe it does not belong; however, it remains a linear equation. In the context of this question, without additional criteria, all of them belong as they are all linear equations. If other characteristics such as positive coefficients or non-fractional coefficients are prioritized, then option D would be the most distinct.