Final answer:
To solve ax = bx, subtract bx from both sides to get (a - b)x = 0. Then divide by (a - b) to find x = 0/(a - b). However, none of the provided options correctly interpret the value of x; x equals 0 if a != b, or any number if a = b.
Step-by-step explanation:
When asked to solve the equation ax = bx for x and interpret the value of the unknown, we start by understanding that a and b are constants, and x is the independent variable. To isolate x, we would subtract bx from both sides to obtain ax - bx = 0, which simplifies to (a - b)x = 0. To find the value of x, we divide both sides by (a - b), giving us x = 0 / (a - b). However, as both terms contain x, if a does not equal to b, we can deduce that x must equal 0 for the equation to be true. On the other hand, if a equals b, then x can be any real number because the equation simplifies to 0 = 0, which is always true. Thus, the correct interpretation is none of the provided options (a), (b), (c), or (d). The value of x depends on the relationship between a and b, but it is not expressed as a direct ratio or difference based on the initial equation given.