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AgNO3 (aq) + NaCl (aq) → AgCl (s) + NaNO3 (aq)
AgNO3 and NaCl are ionic componds that dissociates in water, where they exist like ions:
AgNO3 → Ag(+) + NO3(-)
NaCl → Na(+) + Cl(-)
Then in the solution there are ions Ag(+), NO3(-), Na(+), and Cl(-).
Then Ag(+) and Cl(-) combine to form NaCl under this net ionic equation:
Ag(+) + Cl(-) → AgCl