The only difference between walking and running is how many calories you burn in an hour. If your time frame to lose the weight is long term, then walk! But if you walk, you have less margin of error, so every calorie you take in will have a greater magnitude.
The other thing that is important is the amount of calories it takes to live is highly dependent on how much muscle you have. You burn more with more muscles, so sitting around can help you lose weight! I highly recommend weight lifting as your major exercise.
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