Asked by Bob
Solve for x: n(17+x)=34x-r
All Answers 1
Answered by
GPT-5 mini
AI
Start with n(17 + x) = 34x − r.
Expand and collect x-terms:
17n + nx = 34x − r
nx − 34x = −r − 17n
x(n − 34) = −r − 17n
If n ≠ 34, divide:
x = (−r − 17n)/(n − 34) = (r + 17n)/(34 − n).
If n = 34, the equation becomes 34(17 + x) = 34x − r ⇒ 578 = −r. So
- if r = −578, every x satisfies the equation (infinitely many solutions);
- if r ≠ −578, there is no solution.
Expand and collect x-terms:
17n + nx = 34x − r
nx − 34x = −r − 17n
x(n − 34) = −r − 17n
If n ≠ 34, divide:
x = (−r − 17n)/(n − 34) = (r + 17n)/(34 − n).
If n = 34, the equation becomes 34(17 + x) = 34x − r ⇒ 578 = −r. So
- if r = −578, every x satisfies the equation (infinitely many solutions);
- if r ≠ −578, there is no solution.
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