Help Solving Hard Math Problems: Strategies and Sample Exercises

In math, you have to rely on your foundational skills to solve more complex problems. As you enter junior high and high school, you may want to brush up on basic math terminology and arithmetic. Here are some ideas for remaining successful in math class even as the work gets harder.

Find available tutors

How to Solve Hard Math Problems

Take Careful Notes

When you encounter a difficult math problem in your homework, it can be helpful to refer back to examples from your class notes. Even if the examples in your notes aren't exactly like the homework problem, they may help you figure out what to do. As a result, make sure you actively take notes in class, even if you don't think you'll need them later on. If you still can't figure out the problem, make sure you ask about it in math class the next day.

Learn Definitions

One way to take good notes is to clearly write out definitions for any math terms you may need later. You can copy math vocabulary from the blackboard, your textbook or even from the Internet (as long as it's a reputable site). Keep your handwriting neat and try using a different color pen for the words and the definitions. For instance, you might write the terms in red and the definitions in black. This visual trick can make it easier to read through your notes later.

Find Easy Parts

A lot of hard math problems can be broken down into steps. Sometimes these steps will include very basic math, like addition or single-digit multiplication. Algebraic expressions can often be shortened by combining like terms. They can then be solved by performing several simple math problems with addition, subtraction and multiplication. Ask your teacher for help breaking hard math problems down into more manageable parts.

Solving for Variables

One of the first things you'll need to master in order to succeed in upper level math classes is how to solve for a variable. One example of a problem you might see in pre-algebra is 4 + 3x = 2. In this problem, the letter x is the variable. You can solve this problem by isolating the variable, like this:

4 + 3x = 2
First, subtract four from both sides.
4 - 4+ 3x = 2 - 4
3x = -2
Now, divide both sides by three to isolate the variable.
3x ÷ 3 = -2 ÷ 3
x = -2/3

Practice Problems

Here are a few practice problems. Remember that what you do to one side of the equation, you must do to the other side.

  1. 5 - x = 2
  2. 12 + x = 97
  3. x - 14 = 26
  4. 7 + x = 12
  5. 96 - x = 87


  1. x = 3
  2. x = 85
  3. x = 40
  4. x = 5
  5. x = 9
Did you find this useful? If so, please let others know!

Other Articles You May Be Interested In

  • More Blog Articles
    Creating Your Own Math Problems and Worksheets

    Supplementing your child's math lessons with a few problems and worksheets of your own will help you become better acquainted with his or her curriculum, and will help your child perform better in the classroom. Here are some tips for creating them.

  • More Blog Articles
    Sample Math Worksheet - Simple Addition

    This simple addition worksheet is only a sample to help you format your own practice math problems. Includes answers.

We Found 7 Tutors You Might Be Interested In

Huntington Learning

  • What Huntington Learning offers:
  • Online and in-center tutoring
  • One on one tutoring
  • Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online


  • What K12 offers:
  • Online tutoring
  • Has a strong and effective partnership with public and private schools
  • AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

Kaplan Kids

  • What Kaplan Kids offers:
  • Online tutoring
  • Customized learning plans
  • Real-Time Progress Reports track your child's progress
Online Only


  • What Kumon offers:
  • In-center tutoring
  • Individualized programs for your child
  • Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

Sylvan Learning

  • What Sylvan Learning offers:
  • Online and in-center tutoring
  • Sylvan tutors are certified teachers who provide personalized instruction
  • Regular assessment and progress reports
In-Home, In-Center and Online

Tutor Doctor

  • What Tutor Doctor offers:
  • In-Home tutoring
  • One on one attention by the tutor
  • Develops personlized programs by working with your child's existing homework
In-Home Only


  • What TutorVista offers:
  • Online tutoring
  • Student works one-on-one with a professional tutor
  • Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only

Our Commitment to You

  • Free Help from Teachers

  • Free Learning Materials

  • Helping Disadvantaged Youth