How do I go to blackthorn city?

Well first you need to go to the Lake of Rage which is north of Mahogany Town. When there catch the Red Gyarados which is rampaging. After you catch it go talk to Lance whos also at the lake. Head back to Mahogany Town now and into a building there. You'll see Lance have his Dragonite use hyperbeam. Anyway a secret passage will be revealed. Head down and battle all the rockets and stuff. Come back and battle the gym leader. After thats all done head to Goldenrod City. Head to the underground, to where you can get your picture taken. A Rocket grunt will give you a Team Rocket uniform thinking your a new recruit, now go to the Radio Tower. Once there just beat all the Rockets in the building. After you get everything done in Goldenrod City fly back to Mahogany Town. Head to the right and the guy who wouldn't let you pass before should let you pass now. Keep going until you reach the Ice Path. Make sure you have a Pokemon that know Strength in your party or else you won't be able to get through. After you Make it through the Ice Path you'll be in Blackthorn City.