problem _noun 

1-) source of difficulty

ADJECTIVES & NOUNS

big, great, enormous
・The pollution in the area is a serious problem that needs immediate attention.

serious, grave, acute, significant
・The lack of resources is a significant problem in underdeveloped regions.

minor, little, petty
・A minor problem with the printer caused a slight delay in printing the documents.

complex, complicated, difficult, knotty, thorny
・The scientist is researching a complex problem in the field of quantum mechanics.

main, underlying, basic, major, central
・The main problem with the plan is its lack of funding.

common • widespread • global • growing 
・The flu outbreak has become a widespread problem in the community.

pressing, urgent, immediate
・The lack of clean drinking water is a pressing problem in many developing countries.

unforeseen • potential • specific 
・The project faced unforeseen problems that delayed its completion.

insoluble, insuperable, insurmountable, intractable 
・Climate change is often viewed as an intractable problem due to its global nature.

long-term, long-standing, perennial
・Smoking can lead to serious long-term problems like lung disease and heart issues.

inherent • chronic • persistent • constant • recurring
・The company has been struggling with chronic problems related to mismanagement.

practical • technical • systemic • multifaceted
・Despite his best efforts, he couldn't overcome the technical problem.

attitude, behavioural, emotional, psychological, ethical
・Anxiety and depression are common psychological problems among young adults.

health, physical, sexual • back, heart, knee
・The medical community is focused on finding a cure for this health problem.

drink, drug
・She's struggling with a drink problem.

housing, traffic, transportation, overcrowding, water
・The government implemented policies to address the housing problem.

economic, financial, legal, social, cultural, political, environmental
・Poverty is a significant social problem that governments aim to address.

communication, production, management, software, safety
・The communication problem between departments led to misunderstandings.

area
・The lack of funding has become a problem area for the project.

child 
・The teacher had a challenging time dealing with the problem child in her class.

VERBS 

have
・The computer has a problem with its keyboard.

be, pose, present
・The language barrier could pose a problem for communication.

bring, cause, create
・His actions could bring problems to the team.

face, confront, encounter, run into
・It's not easy, but we must face the problem and find a solution.

be faced with, be confronted by/with, be beset with, be dogged by, be fraught with
・The construction project was beset with problems from the beginning.

raise 
・He raised a problem about the fairness of the competition.

identify • understand • explain
・We need to identify the root of the problem.

discuss, consider, debate, look at/into
・Let's sit down and discuss the problem at hand.

analyse, examine, investigate, explore
・Experts are examining the problem to determine the best course of action.

address, handle, tackle, approach, attack, combat, come/get to grips with, grapple with
・It's important to address this problem before it escalates.
・The healthcare system is grappling with the problem of rising medical costs.

avoid, find a way around/round, get around/round, circumvent
・Following safety guidelines can help you avoid problems.

ignore • prevent
・Trying to ignore the problem only worsened it.
・Regular maintenance can help prevent such problems from arising.

solve, fix, resolve, overcome, deal with, clear up, cure
・The team is working together to fix the software problem.

alleviate, ease, reduce
・Repairing the equipment will alleviate the problem.

exacerbate, aggravate, worsen, complicate
・His approach aggravated the problem further.

PROBLEM + VERB 
arise, occur, come up
・The problem may arise from miscommunication.

exist
・Solutions are needed where problems exist.

remain, persist
・The problem of pollution persists globally.

face sb, confront sb
・The main problem we're currently facing is lack of resources.

lie in 
・The key to solving the problem may lie in addressing the root cause.

require, demand
・The problem of inequality requires systemic changes in society.

PREPOSITIONS

about
・There's a problem about the noise level in the neighborhood.

for 
・Time management can be a problem for students during exams.

of 
・The problem of inequality remains a societal challenge.

with
・The car had a problem with its engine.
・She has a problem with someone on the team.

PHRASES

a solution to a problem, a remedy to a problem
・Don't worry, we can find a solution to this problem.

the crux/heart/root of the problem
・Addressing the root of the problem can lead to effective solutions.

the scale of a problem
・We need to assess the scale of the problem before deciding on a solution.

problem-solving
・Adopting a systematic approach to problem-solving yields better results.

an approach to a problem
・Let's brainstorm different ideas for an optimal approach to this problem.

2-) question

ADJECTIVES

difficult, complicated
・The students worked together to solve the difficult math problem.

easy, simple
・The teacher assigned an easy problem for homework.

mathematical, math
 ・I need help with this mathematical problem from my homework.

VERBS

solve, do, find the answer to
・Can you help me do this math problem?