What is Algebra?

Algebra is like a puzzle where we use letters and numbers to represent a relationship. The letters (like ( x ) and ( y )) are called variables. They can stand for different numbers.

Why Do We Use Algebra?

Algebra helps us solve problems and understand relationships between different quantities. For example, if you want to know how much money you’ll have after saving £5 each week, you can use algebra to express it.

Key Rules in Algebra

  1. Variables: Letters that stand for numbers, like ( x ) or ( y ).
  2. Constants: These are fixed numbers, like 5, 10, or -2.
  3. Expressions: A combination of variables and constants, like ( 3x + 5 ).
  4. Equations: A statement that two expressions are equal, like ( 2x + 3 = 11 ).

Simple Steps to Solve Equations

When solving equations, remember these steps:

  1. Isolate the variable: Get ( x ) or any other variable by itself on one side.
  2. Perform the opposite operation: If you see ( + 3 ), do ( – 3 ) to both sides. If it’s ( \times 2 ), do ( \div 2 ) to both sides.
  3. Check your work: Put the value back into the original equation to make sure it works.

Example

Let’s solve the equation ( 2x + 3 = 11 ).

  1. Subtract 3 from both sides:$$ 2x + 3 – 3 = 11 – 3 $$This simplifies to:$$ 2x = 8 $$
  2. Divide both sides by 2:$$ \frac{2x}{2} = \frac{8}{2} $$This gives us:$$ x = 4 $$
  3. Check your answer:Substitute ( x ) back into the original equation:$$ 2(4) + 3 = 11 $$$$ 8 + 3 = 11 $$It works!

Tips & Tricks

  • Keep it balanced: Whatever you do to one side of the equation, do to the other side.
  • Practice makes perfect: The more problems you solve, the easier it gets!
  • Use visual aids: Drawing a number line or using counters can help you understand equations better.

Practice Questions

Easy Level Questions

  1. Solve for ( x ): ( x + 5 = 10 )
  2. Solve for ( x ): ( 3x = 12 )
  3. Solve for ( y ): ( y – 2 = 6 )
  4. Solve for ( x ): ( 5 + x = 15 )
  5. Solve for ( x ): ( 7x = 28 )
  6. Solve for ( y ): ( 10 = y + 4 )
  7. Solve for ( x ): ( x – 3 = 0 )
  8. Solve for ( x ): ( 4 + x = 9 )
  9. Solve for ( x ): ( 2x = 6 )
  10. Solve for ( y ): ( y + 8 = 12 )
  11. Solve for ( x ): ( 6x = 36 )
  12. Solve for ( z ): ( z – 4 = 2 )
  13. Solve for ( x ): ( 2 + x = 5 )
  14. Solve for ( x ): ( 9 = x + 3 )
  15. Solve for ( x ): ( x + 1 = 6 )
  16. Solve for ( y ): ( 3y = 15 )
  17. Solve for ( x ): ( 8 = x + 2 )
  18. Solve for ( z ): ( z + 5 = 10 )
  19. Solve for ( x ): ( x – 6 = -2 )
  20. Solve for ( y ): ( y + 10 = 20 )

Medium Level Questions

  1. Solve for ( x ): ( 2x + 3 = 11 )
  2. Solve for ( y ): ( 4y – 5 = 11 )
  3. Solve for ( z ): ( z/3 + 4 = 7 )
  4. Solve for ( x ): ( 5x – 3 = 12 )
  5. Solve for ( y ): ( 3y + 6 = 15 )
  6. Solve for ( x ): ( 4(x + 2) = 20 )
  7. Solve for ( x ): ( 2x – 4 = 10 )
  8. Solve for ( y ): ( 7y + 2 = 23 )
  9. Solve for ( x ): ( 10 – 2x = 4 )
  10. Solve for ( z ): ( 3(z – 1) = 12 )
  11. Solve for ( x ): ( 6 = 2x + 2 )
  12. Solve for ( y ): ( y/2 – 3 = 0 )
  13. Solve for ( x ): ( 5 = x/4 + 3 )
  14. Solve for ( y ): ( 8y = 32 – 4 )
  15. Solve for ( x ): ( x + 2x = 15 )
  16. Solve for ( z ): ( z + 5z = 30 )
  17. Solve for ( x ): ( 1 + 2x = 9 )
  18. Solve for ( y ): ( 2y + 10 = 0 )
  19. Solve for ( x ): ( 3(x – 2) = 6 )
  20. Solve for ( y ): ( 10 – y = 4 )

Hard Level Questions

  1. Solve for ( x ): ( 2(x + 3) = 4x – 6 )
  2. Solve for ( y ): ( 3y + 4 = 2y – 1 )
  3. Solve for ( z ): ( 7 – 2(z + 1) = 3 )
  4. Solve for ( x ): ( 4(2x – 1) = 8 )
  5. Solve for ( y ): ( 5y – 3 = 2y + 6 )
  6. Solve for ( x ): ( 3(x – 4) = 2(x + 1) )
  7. Solve for ( z ): ( 8z + 4 = 3(2z + 1) )
  8. Solve for ( x ): ( 5(x + 2) – 3x = 10 )
  9. Solve for ( y ): ( 2y + 3(2 – y) = 9 )
  10. Solve for ( x ): ( 4x/2 + 3 = 5 )
  11. Solve for ( y ): ( y/3 – 1 = 2y/4 + 2 )
  12. Solve for ( x ): ( 2(3x – 4) + 3 = 5 )
  13. Solve for ( z ): ( 6(z – 1) + 2 = 2(z + 3) )
  14. Solve for ( x ): ( 5x – 2(3x + 4) = 8 )
  15. Solve for ( y ): ( 4y + 2 = y – 9 )
  16. Solve for ( x ): ( 3(x + 5) = 2(5 – x) )
  17. Solve for ( z ): ( 2(z + 4) = 3(z – 2) + 10 )
  18. Solve for ( x ): ( 8x – 2(3 – 2x) = 16 )
  19. Solve for ( y ): ( y + 2(y + 1) = 5y – 4 )
  20. Solve for ( x ): ( 10 = 2(x + 1) + 4(x – 1) )

Answers and Explanations

Easy Level Answers

  1. ( x = 5 )
  2. ( x = 4 )
  3. ( y = 8 )
  4. ( x = 10 )
  5. ( x = 4 )
  6. ( y = 6 )
  7. ( x = 3 )
  8. ( x = 5 )
  9. ( x = 3 )
  10. ( y = 2 )
  11. ( x = 6 )
  12. ( z = 6 )
  13. ( x = 3 )
  14. ( x = 6 )
  15. ( x = 5 )
  16. ( y = 5 )
  17. ( x = 6 )
  18. ( z = 5 )
  19. ( x = 4 )
  20. ( y = 10 )

Medium Level Answers

  1. ( x = 4 )
  2. ( y = 4 )
  3. ( z = 9 )
  4. ( x = 3 )
  5. ( y = 3 )
  6. ( x = 3 )
  7. ( x = 7 )
  8. ( y = 3 )
  9. ( x = 3 )
  10. ( z = 5 )
  11. ( x = 2 )
  12. ( y = 6 )
  13. ( y = 20 )
  14. ( x = 5 )
  15. ( z = 5 )
  16. ( x = 4 )
  17. ( y = -6 )
  18. ( x = 4 )
  19. ( y = 6 )
  20. ( y = 6 )

Hard Level Answers

  1. ( x = 5 )
  2. ( y = -5 )
  3. ( z = 1 )
  4. ( x = 2 )
  5. ( y = 3 )
  6. ( x = 10 )
  7. ( z = 2 )
  8. ( x = 4 )
  9. ( y = 0 )
  10. ( x = 1 )
  11. ( y = 12 )
  12. ( x = 7 )
  13. ( z = 4 )
  14. ( x = 6 )
  15. ( y = -3 )
  16. ( x = -5 )
  17. ( z = 2 )
  18. ( x = 4 )
  19. ( y = 3 )
  20. ( x = 3 )

Feel free to ask questions! Remember, practice is key to mastering algebra!