In this example, it is "solve the problem" because they're "taking steps." Taking steps implies they are taking action in this case. The sentence can be rewritten as: City and state officials say they`re taking action to solve the problem but residents of Newark say for years, their leaders have denied there was a problem.

Addressing the problem is taking an action to solve a problem. For example: Sam wants to buy a car, but he has not got enough money. And this is a problem for Sam. To address this problem Sam decides to find a job.

Hi Hongju! "address the problem" means "solve the problem" IF there was an actual solution at the moment/instant solution. Yet, "address the problem" 's actual meaning in a sentence is "DEAL WITH the problem, meaning it doesn't have an actual solution the the moment, but there's a way to solve it and it will take time. [or] The solution to the problem is not instant, so in this sentence: " ...taking steps to address the problem.." Have a great day!

"Addressing the problem" is not solving it. To address the problem means that people are taking steps to solve it. The problem is not solved yet (and it may never be solved, but it is being "addressed" or "dealt with" or "handled"). The second definition you have is more correct. Attention is being paid to the problem. Another way of saying "they are addressing the problem" is "they are dealing with the problem," "they are handling the problem," or "they are working on the problem." In the sentence, "City and state officials say they`re taking steps to address the problem ...," it means that the officials say they are working on a solution for the problem.