Final answer:
Any of the three equations A) x + 16 = 4x - 5, B) x + 16 + 4x - 5 = 90, or C) x + 16 + 4x - 5 = 180 can be set up to solve for x, as they are all linear and can be simplified to the form y = mx + b. The choice of equation depends on the context of the problem.
Step-by-step explanation:
The student is dealing with a topic in Mathematics, specifically related to linear equations and potentially quadratic equations. The first step is to determine whether the equations provided are linear, and this can be done by checking if they can be expressed in the form y = mx + b, where m and b are constants. Looking at the equations presented:
- A) x + 16 = 4x - 5 can be re-arranged to the form of a linear equation by collecting like terms.
- B) x + 16 + 4x - 5 = 90 is also linear as it simplifies to a form with x as the only variable on one side.
- C) x + 16 + 4x - 5 = 180 is similar to B and is also linear.
Therefore, any of these equations can be set up to solve for x. However, the context of the problem will determine which equation to use. If the context suggests an angle measurement (perhaps in a geometry problem), then one might consider sums to 180 degrees for equation C). Without additional context, equations A) and B) seem more straightforward for solving for a single variable.