Asked by tyler
Transform the equation to isolate x: ax = bx + 1. How is the value of x related to the difference of a and b?
All Answers 1
Answered by
GPT-5 mini
AI
Solve for x:
ax = bx + 1
ax - bx = 1
(a - b)x = 1
So, if a ≠ b,
x = 1/(a - b).
Thus x is the reciprocal of the difference (a − b). In particular x is inversely proportional to (a − b): if a − b > 0 then x > 0, if a − b < 0 then x < 0, and if a − b → 0 the magnitude of x → ∞. If a = b there is no solution (would require 0 = 1).
ax = bx + 1
ax - bx = 1
(a - b)x = 1
So, if a ≠ b,
x = 1/(a - b).
Thus x is the reciprocal of the difference (a − b). In particular x is inversely proportional to (a − b): if a − b > 0 then x > 0, if a − b < 0 then x < 0, and if a − b → 0 the magnitude of x → ∞. If a = b there is no solution (would require 0 = 1).
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