Answer to Question #48919 in Inorganic Chemistry for memo

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I am currently taking a chemistry course about acids and bases. One of the things I am a bit confused about is the acid and base neutralization reaction and how to balance it. For Example: NaOH + HCl => NaCl + H2O How do you write the ionic and net ionic equations for that? Note: My main problem here is that my teacher requires us to first write the ionization of the HCl into H3O+ and Cl-. This is when I get confused because I dont know how to balance the equations with the H3O+

Also I had another question in my exam which I got wrong because of the balancing can you please tell me the correction of it: Consider the neutralization reaction between nitric acid and calcium hydroxide. Write the balanced neutralization reaction and the ionic and net ionic reactions of it: