Question

what equation would match the solution set of {5}?

x + x - 9 = 1 + x
x^2 - 10 = 15
3^x/5 + 4 = 7
2x - 20 = 30

Answer 1

As written, none of the four equations has solution set exactly {5}.

Quick checks:
- x + x − 9 = 1 + x → 2x − 9 = 1 + x → x = 10.
- x^2 − 10 = 15 → x^2 = 25 → x = ±5 (so solution set {−5, 5}, not {5}).
- (3^x)/5 + 4 = 7 → 3^x = 15 → x = log_3(15) ≈ 2.465 (not 5).
- 2x − 20 = 30 → 2x = 50 → x = 25.

However, if the intended equation was 3^(x/5) + 4 = 7 (i.e., 3 to the power (x/5)), then
3^(x/5) + 4 = 7 → 3^(x/5) = 3 → x/5 = 1 → x = 5,
so 3^(x/5) + 4 = 7 would have solution set {5}.

Which formatting did you mean for the third equation?