Answer: They replied, "Believe in the Lord Jesus,
and you will be saved," (verse 31).
MORE INFORMATION AND/OR OTHER SCRIPTURE REFERENCES:
Mark 16:16: [Jesus said,] "Whoever
believes and is baptized will be saved, but whoever does not
believe will be condemned."
John 3:14-18: [Jesus said,] "Just
as Moses lifted up the snake in the desert, so the Son of Man must
be lifted up, that everyone who believes in Him may have eternal
life. For God so loved the world that He gave His One and
Only Son, that whoever believes in Him shall not perish but have
eternal life. For God did not send His Son into the world to
condemn the world, but to save the world through Him. Whoever
believes in Him is not condemned, but whoever does not believe
stands condemned already because he has not believed in the Name of
God's One and Only Son."
Acts 11:13-14: "He [Cornelius] told
us how he had seen an angel appear in his house and say,
'Send to Joppa for Simon who is called Peter. He will
bring you a message through which you and all your household will
be saved.'"
From
The Acts of the Apostles From Jerusalem to Rome by Wayne
Jackson:
Whatever the case, his [the jailer's] knowledge is
rudimentary. He thus was told: "Believe on the
Lord Jesus, and you shall be saved; you and your
family." The aorist imperative tense is probably
ingressive, i.e., start believing on the Lord. It has
been suggested that the imperative (command mood), when joined with
the future, constitutes a Hebraic conditional sentence (Rienecker,
305), i.e., believing was preliminary to his salvation.
Salvation is not unconditional, as some allege. This passage
provides no evidence, however, for a "faith only"
redemption. The sort of belief in view is that which operates in
doing the Lord's Will (cf. John 3:36
ASV; Galatians 5:6; Hebrews
5:8-9).
And so applies the Scripture: "How, then, can
they call on the One they have not believed in? And how can they
believe in the One of Whom they have not heard? And how can they
hear without someone preaching to them?" (Romans
10:14).