You are at a meeting for the homeowners' association for your neighborhood. You have made a suggestion to raise the homeowner's fee, but the other members immediately started making noises and complaining before you could explain your reasons for raising it. You want everyone to listen to your reasons first before deciding, so you say:
Hold on. Just hear me out first.
This means "Wait" — especially when someone doesn't seem to want to wait:
Hold on. Wait for me!
This phrase means to listen to someone's complete explanation before making a conclusion about a topic. If someone won't listen to your explanation, you can say:
She wouldn't even hear me out.
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